Roulette 1 number

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January 26th, 2020 at 11:19:30 AM permalink

Quote: masterj
Hello all,

the expected frequency of won bets on 1 number of a European Roulette Wheel is p=1/37.
In the long run, you should get this result. (e.g. you win 1000 out of 37000 spins.

What are the deviations after x spins? It would be great if someone could tell me how I can calculate this?

Thank you very much,

Well, statistics isn't my strong suit, but I think standard deviation is calculated like this:

SD = square root of variance

Oh, you want more?
In this case, variance = the sum of p(k) (v(k) - m)², where k is each of the n possible results; p(k) is the probability that result k happens, v(k) is the value of result k, and m is the mean result.
In this case, for one spin, there are two possible results; 1, with probability 1/37, and 0, with probability 36/37.
This means p(1) = 1/37, v(1) = 1, p(2) = 36/37, v(2) = 0, and m = 1/37.
The variance = 1/37 x (1 - 1/37)² + 36/37 x (0 - 1/37)² = (36² + 36) / 37³
= (36 x 37) / 37³ = (6 / 37)²
and the standard deviation is the square root of this, or 6/37.

For x spins, there are (x + 1) possibile results - 0 hits, 1 hit, 2 hits, ..., (x - 1) hits, and x hits.
The probability of n hits is (x)C(n) (1/37)^x (36/37)^n-x, where (x)C(n) is the number of combinations of x items taken n at a time (also COMBIN(x,n) or C(x,n)); the value of n hits is n, and the mean in x spins is x/37.

If I am calculating this right, after X spins, the mean number of hits is X / 37, and the standard deviation is 6 sqrt(X) / 37.
Note that, while the standard deviation of 37,000 spins is about 31.2, the standard deviation of 74,000 spins is not twice that, but about 1.4 times that.

masterj

masterj

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January 26th, 2020 at 11:45:21 AM permalink

Wow, that was quick! Thx man!

I have got some questions to your calculations,

and the standard deviation is the square root of this, or 6/37.
Question: does this mean that 6/37 is that you can run over / under expected value of +5 on average?

Note that, while the standard deviation of 37,000 spins is about 31.2, the standard deviation of 74,000 spins is not twice that, but about 1.4 times that.
Question: does this mean that after 37000 spins, there is a chance that 1 number runs over / under the expected value of 31.2 spins?

Thank you very much again!

ThatDonGuy

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January 26th, 2020 at 12:01:21 PM permalink

Quote: masterj
Wow, that was quick! Thx man!

I have got some questions to your calculations,

and the standard deviation is the square root of this, or 6/37.
Question: does this mean that 6/37 is that you can run over / under expected value of +5 on average?

Note that, while the standard deviation of 37,000 spins is about 31.2, the standard deviation of 74,000 spins is not twice that, but about 1.4 times that.
Question: does this mean that after 37000 spins, there is a chance that 1 number runs over / under the expected value of 31.2 spins?

Thank you very much again!

6/37 is the standard deviation over one spin. For N spins, the standard deviation for the number of hits of a particular number is 6 sqrt(N) / 37.

There is about a 68% chance that a set of results will be within one standard deviation either way (i.e. anywhere from one SD below the mean to one SD above), and about a 95% chance that the results will be within two SDs either way. The exact value for N SDs is 200 sqrt(2 PI) times the integral from 0 to positive infinity of the function 1 / (e to the power of N²); however, there is no known "easy " way to calculate that - you have to use approximation methods.

For example, over 10,000 spins, the expected number of times 1 will come up is 10,000 / 37 = 270.27, and the standard deviation is 600 / 37 = 16.22, so 65% of the time, 1 should come up between 254.05 and 286.49 times, and 98% of the time, 1 should come up between 237.83 and 302.71 times.

Pardon me for asking, but why the interest in this particular situation?

Given 37,000 spins, it's almost certain that at least one number will go over the expected number of 1000 spins - in fact, the only way that no numbers have more than 1000 hits (and, for that matter, none have fewer than 1000) is if every number comes up 1000 times, which, despite being "expected," is almost impossible.

masterj

masterj

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January 27th, 2020 at 12:58:49 AM permalink

For example, over 10,000 spins, the expected number of times 1 will come up is 10,000 / 37 = 270.27, and the standard deviation is 600 / 37 = 16.22, so 65% of the time, 1 should come up between 254.05 and 286.49 times, and 98% of the time, 1 should come up between 237.83 and 302.71 times.

Pardon me for asking, but why the interest in this particular situation?

if you choose 1 out of 37 numbers, most of them are within one SD. if you can make a bigger profit with these numbers, then you loose on numbers within 2 SD, then it might be possible to make some money.

charliepatrick

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January 27th, 2020 at 1:25:27 AM permalink

For a two way result where the chances of winning are p and losing are q = (1-p) then the average is Np and the SD = SQRT (Npq). However for small N you can also work out the probabilities exactly by Pr(0) = 36/37 ^ N etc.

weezrDASvegas

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January 27th, 2020 at 2:33:52 AM permalink

Quote: masterj
Hello all,

the expected frequency of won bets on 1 number of a European Roulette Wheel is p=1/37.
In the long run, you should get this result. (e.g. you win 1000 out of 37000 spins.

What are the deviations after x spins? It would be great if someone could tell me how I can calculate this?

Thank you very much,

The roulette numbers will never come out equally. Its like the lotto numbers. they come out close to one another only in percentages after lots of draws. The standard deviation separates them in absolute terms. it is called the normal probability rule. One app does good calculations (search SuperFormula).

For 1000 spins you got

The standard deviation for an event of probability
p = .02702703
in 1000 binomial experiments is:
BSD = 5.13

The expected (theoretical) number of successes is: 27

Based on the Normal Probability Rule:

* 68.2% of the successes will fall within 1 Standard Deviation
from 27 - i.e., between 22 - 32
* 95.4% of the successes will fall within 2 Standard Deviations
from 27 - i.e., between 17 - 37
* 99.7% of the successes will fall within 3 Standard Deviations
from 27 - i.e., between 12 - 42
I submit to you that no roulette number will show fewer than 12 hits and no more than 42 wins. That happens 99.7% of the times.

I saw results for about 8000 real spins from a German casino (I think the only who publishes roulette resulst).

The standard deviation for an event of probability
p = .02702703
in 7990 binomial experiments is:
BSD = 14.5

The expected (theoretical) number of successes is: 216

Based on the Normal Probability Rule:

* 68.2% of the successes will fall within 1 Standard Deviation
from 216 - i.e., between 202 - 230
* 95.4% of the successes will fall within 2 Standard Deviations
from 216 - i.e., between 188 - 244
* 99.7% of the successes will fall within 3 Standard Deviations
from 216 - i.e., between 174 - 258

The coldest number had 192 hits and the hottest won 239 wins � inside the calculated limits. It is convincing that you can win at roulette with particular numbers * you might find the bias *
https://download.saliu.com/roulette-systems.html
Roulette Numbers Ranked by Frequency

weezrDASvegas

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January 27th, 2020 at 2:43:06 AM permalink

Quote: weezrDASvegas
The roulette numbers will never come out equally. Its like the lotto numbers. they come out close to one another only in percentages after lots of draws. The standard deviation separates them in absolute terms. it is called the normal probability rule. One app does good calculations (search SuperFormula).

For 1000 spins you got

The standard deviation for an event of probability
p = .02702703
in 1000 binomial experiments is:
BSD = 5.13

The expected (theoretical) number of successes is: 27

Based on the Normal Probability Rule:

* 68.2% of the successes will fall within 1 Standard Deviation
from 27 - i.e., between 22 - 32
* 95.4% of the successes will fall within 2 Standard Deviations
from 27 - i.e., between 17 - 37
* 99.7% of the successes will fall within 3 Standard Deviations
from 27 - i.e., between 12 - 42
I submit to you that no roulette number will show fewer than 12 hits and no more than 42 wins. That happens 99.7% of the times.

I saw results for about 8000 real spins from a German casino (I think the only who publishes roulette resulst).

The standard deviation for an event of probability
p = .02702703
in 7990 binomial experiments is:
BSD = 14.5

The expected (theoretical) number of successes is: 216

Based on the Normal Probability Rule:

* 68.2% of the successes will fall within 1 Standard Deviation
from 216 - i.e., between 202 - 230
* 95.4% of the successes will fall within 2 Standard Deviations
from 216 - i.e., between 188 - 244
* 99.7% of the successes will fall within 3 Standard Deviations
from 216 - i.e., between 174 - 258

The coldest number had 192 hits and the hottest won 239 wins � inside the calculated limits. It is convincing that you can win at roulette with particular numbers * you might find the bias *
https://download.saliu.com/roulette-systems.html
Roulette Numbers Ranked by Frequency

If you average the coldest and hottest numbers you get the expected number of successes (216)

192+239=431 average 215.5~216

masterj

masterj

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January 27th, 2020 at 6:41:43 AM permalink

Hello weezrDASvegas,

The standard deviation for an event of probability
p = .02702703
in 7990 binomial experiments is:
BSD = 14.5

The expected (theoretical) number of successes is: 216

Based on the Normal Probability Rule:

* 68.2% of the successes will fall within 1 Standard Deviation
from 216 - i.e., between 202 - 230
* 95.4% of the successes will fall within 2 Standard Deviations
from 216 - i.e., between 188 - 244
* 99.7% of the successes will fall within 3 Standard Deviations
from 216 - i.e., between 174 - 258

do these deviations get smaller or bigger the more spins you play?

weezrDASvegas

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January 27th, 2020 at 8:02:10 AM permalink

Quote: masterj
Hello weezrDASvegas,

The standard deviation for an event of probability
p = .02702703
in 7990 binomial experiments is:
BSD = 14.5

The expected (theoretical) number of successes is: 216

Based on the Normal Probability Rule:

* 68.2% of the successes will fall within 1 Standard Deviation
from 216 - i.e., between 202 - 230
* 95.4% of the successes will fall within 2 Standard Deviations
from 216 - i.e., between 188 - 244
* 99.7% of the successes will fall within 3 Standard Deviations
from 216 - i.e., between 174 - 258

do these deviations get smaller or bigger the more spins you play?

standard deviation gets BIGGER and B I G G E R the more spins you play. the gaps between roulette numbers get bigger although percentages get closer.

100 spins - SD = 1.6
1000 spins - SD = 5.13
7990 spins - SD = 14.5
37000 spins - SD = 31.2

SuperFormula.exe calculates

The standard deviation for an event of probability
p = .02702703
in 37000 binomial experiments is:
BSD = 31.19

The expected (theoretical) number of successes is: 1000

Based on the Normal Probability Rule:

* 68.2% of the successes will fall within 1 Standard Deviation
from 1000 - i.e., between 969 - 1031
* 95.4% of the successes will fall within 2 Standard Deviations
from 1000 - i.e., between 938 - 1062
* 99.7% of the successes will fall within 3 Standard Deviations
from 1000 - i.e., between 907 - 1093

You can expect no fewer than 907 wins but no more than 1093 hits. hopefully you'll be on the righthand side
https://saliu.com/scientific-software.html
Scientific Software for Mathematics, Probability, Odds

Ace2

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January 27th, 2020 at 10:14:01 AM permalink

To calculate the probability of getting exactly 1000 wins in 37000, a useful approximation is:

1 / (1000 * 36/37 * 2 * PI)^.5 = 1.28%

For this many trials, the estimate is accurate to at least 16 digits (as far as my excel goes) relative to the probability mass function.

Last edited by: Ace2 on Jan 27, 2020

It�s all about making that GTA

weezrDASvegas

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January 27th, 2020 at 1:28:45 PM permalink

Quote: Ace2
To calculate the probability of getting exactly 1000 wins in 37000, a useful approximation is:

1 / (1000 * 36/37 * 2 * PI)^.5 = 1.28%

For this many trials, the estimate is accurate to at least 16 digits (as far as my excel goes) relative to the probability mass function.

SuperFormula.exe calculus

exactly 1000 wins in 37000 spins: 1 in 2.50991163241154E+1058
at least 1000 wins in 37000 spins: 1 in 2.45739805052973E+1058

you can bet all your babymilk money that it would never happen.. its like 1 in (25followed by 1057 zeros)... the norm never happens absolutely.. but you can seriously hope you gonna be on the righthand side.. just follow the trend�

Ace2

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January 27th, 2020 at 1:52:16 PM permalink

Reasonableness test. For 37000 spins we know the expectation is 1000 wins, and with a SD of 31 we know there�s a 68% chance the result will be between 969 and 1031. So 68% / 62 values in that range is an average of 1.1 % per value.

Obviously those are not equally distributed with values closer to the mean being higher. 1.28% seems reasonable.

Above or below the mean will be (100 - 1.28) / 2 = 49.36%

How do you justify 2.5 * 10^1058?

It�s all about making that GTA

weezrDASvegas

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January 27th, 2020 at 2:22:11 PM permalink

Quote: Ace2
Reasonableness test. For 37000 spins we know the expectation is 1000 wins, and with a SD of 31 we know there�s a 68% chance the result will be between 969 and 1031. So 68% / 62 values in that range is an average of 1.1 % per value.

Obviously those are not equally distributed with values closer to the mean being higher. 1.28% seems reasonable.

Above or below the mean will be (100 - 1.28) / 2 = 49.36%

How do you justify 2.5 * 10^1058?

�How do you justify 2.5 * 10^1058?�

I guess its maths.. �exactly M successes in N trials� in SuperFormula.exe. take sum easier case like cointoss
Exactly 1000 heads in 37000 tosses
1 in 1708175116

Exactly is very HARD to get� the more successes the harder it gets for exactly one success... your calculations are� i don�t know how you came up with them??

If you sez 1000 wins in 37000 spins probability is 49.36%??? well� you bettah check your pulse.. you never get that probability.. run any random generators: you never see a roulette number with 1000 hits in 37000 spins. run this free roulette generator
https://saliu.com/bbs/messages/301.html
Online Roulette Number Generator

weezrDASvegas

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January 27th, 2020 at 4:18:26 PM permalink

Quote: weezrDASvegas
�How do you justify 2.5 * 10^1058?�

I guess its maths.. �exactly M successes in N trials� in SuperFormula.exe. take sum easier case like cointoss
Exactly 1000 heads in 37000 tosses
1 in 1708175116

Exactly is very HARD to get� the more successes the harder it gets for exactly one success... your calculations are� i don�t know how you came up with them??

If you sez 1000 wins in 37000 spins probability is 49.36%??? well� you bettah check your pulse.. you never get that probability.. run any random generators: you never see a roulette number with 1000 hits in 37000 spins. run this free roulette generator
https://saliu.com/bbs/messages/301.html
Online Roulette Number Generator

Maybe that SuperFormula.exe is limited to some 1750 max trials. but we can calculate for fewer trials and the simple coin toss.

* exactly 5 successes in 10 trials: 24.6% (you might figure 50%)
* exactly 50 successes in 100 trials: 8% (you might figure 50%)
* exactly 500 successes in 1000 trials: 2.5% (you might figure 50%)
* exactly 1000 successes in 1750 trials: 1 in 3140653769.

So the more successes the harder it gets for exactly one success...

Ace2

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January 27th, 2020 at 4:24:22 PM permalink

You might want to reread the title of this thread. It�s not about coin tosses

It�s all about making that GTA

weezrDASvegas

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January 27th, 2020 at 4:25:51 PM permalink

Quote: weezrDASvegas
Quote: weezrDASvegas
�How do you justify 2.5 * 10^1058?�

I guess its maths.. �exactly M successes in N trials� in SuperFormula.exe. take sum easier case like cointoss
Exactly 1000 heads in 37000 tosses
1 in 1708175116

Exactly is very HARD to get� the more successes the harder it gets for exactly one success... your calculations are� i don�t know how you came up with them??

If you sez 1000 wins in 37000 spins probability is 49.36%??? well� you bettah check your pulse.. you never get that probability.. run any random generators: you never see a roulette number with 1000 hits in 37000 spins. run this free roulette generator
https://saliu.com/bbs/messages/301.html
Online Roulette Number Generator

Maybe that SuperFormula.exe is limited to some 1750 max trials. but we can calculate for fewer trials and the simple coin toss.

* exactly 5 successes in 10 trials: 24.6% (you might figure 50%)
* exactly 50 successes in 100 trials: 8% (you might figure 50%)
* exactly 500 successes in 1000 trials: 2.5% (you might figure 50%)
* exactly 1000 successes in 1750 trials: 1 in 3140653769.

So the more successes the harder it gets for exactly one success...

Maybe that SuperFormula.exe is limited to some 1750 max trials. but we can calculate for fewer trials and the simple coin toss.

* exactly 5 successes in 10 trials: 24.6% (you might figure 50%)
* exactly 50 successes in 100 trials: 8% (you might figure 50%)
* exactly 500 successes in 1000 trials: 2.5% (you might figure 50%)
* exactly 1000 successes in 1750 trials: 1 in 3140653769.

So the more successes the harder it gets for exactly one success...

I just read �
There is a data size limit. The number of trials N must not be larger than 1754. There will be an overflow if you use very large numbers. The factorials grow crazily high and fast!
The generalized formula for exactly M successes in N trials:

BDF = C(N, M) * pM * [(1 � p)]^(N � M)

https://saliu.com/formula.html
Software for Probability, Odds, Statistics, Gambling

weezrDASvegas

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January 27th, 2020 at 4:39:32 PM permalink

Quote: Ace2
You might want to reread the title of this thread. It�s not about coin tosses

�You might want to reread the title of this thread. It�s not about coin tosses�

Exactlymundo! That�s what I thought mah man. the odds for roulette are even sharper against 1000 hits by a roulette number in 37000 spins. its �exactly� like the more successes the harder it gets for exactly one success... far from 49.36% for one roulette number to record 1000 hits in 37000 spins� no way�

ThatDonGuy

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January 27th, 2020 at 4:44:30 PM permalink

Quote: weezrDASvegas
�How do you justify 2.5 * 10^1058?�

I guess its maths.. �exactly M successes in N trials� in SuperFormula.exe. take sum easier case like cointoss
Exactly 1000 heads in 37000 tosses
1 in 1708175116

It's not that hard; I get 1 in 78.2.

Here's how:
The probability of getting 1000, say, zeroes in 37,000 spins of a single-zero wheel is (37,000)C(1000) x (1/37)¹⁰⁰⁰ x (36/37)^36,000
Most methods of calculating this would result in arithmetic overflows, but if you use logarithms and a spreadsheet, you can do it.

(37,000)C(1000) = 37,000 / 1 x 36,999 / 2 x 36,998 / 3 x ... x 36,002 / 999 x 36,001 / 1000
log ((37,000)C(1000)) = log 37,000 - log 1 + log 36,999 - log 2 + ... + log 36,001 - log 1000

(1/37)¹⁰⁰⁰ x (36/37)^36,000 = 36^36,000 / 37^37,000
log ((1/37)¹⁰⁰⁰ x (36/37)^36,000) = 36,000 log 36 - 37,000 log 37

log ((37,000)C(1000) x (1/37)¹⁰⁰⁰ x (36/37)^36,000) = log ((37,000)C(1000)) + log (1/37)¹⁰⁰⁰ x (36/37)^36,000)
= log 37,000 - log 1 + log 36,999 - log 2 + ... + log 36,001 - log 1000 + 36,000 log 36 - 37,000 log 37

(37,000)C(1000) x (1/37)¹⁰⁰⁰ x (36/37)^36,000 = 10 to the power of (log 37,000 - log 1 + log 36,999 - log 2 + ... + log 36,001 - log 1000 + 36,000 log 36 - 37,000 log 37) = about 1 / 78.19456.

weezrDASvegas

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January 27th, 2020 at 4:58:57 PM permalink

Quote: ThatDonGuy
It's not that hard; I get 1 in 78.2.

Here's how:
The probability of getting 1000, say, zeroes in 37,000 spins of a single-zero wheel is (37,000)C(1000) x (1/37)¹⁰⁰⁰ x (36/37)^36,000
Most methods of calculating this would result in arithmetic overflows, but if you use logarithms and a spreadsheet, you can do it.

(37,000)C(1000) = 37,000 / 1 x 36,999 / 2 x 36,998 / 3 x ... x 36,002 / 999 x 36,001 / 1000
log ((37,000)C(1000)) = log 37,000 - log 1 + log 36,999 - log 2 + ... + log 36,001 - log 1000

(1/37)¹⁰⁰⁰ x (36/37)^36,000 = 36^36,000 / 37^37,000
log ((1/37)¹⁰⁰⁰ x (36/37)^36,000) = 36,000 log 36 - 37,000 log 37

log ((37,000)C(1000) x (1/37)¹⁰⁰⁰ x (36/37)^36,000) = log ((37,000)C(1000)) + log (1/37)¹⁰⁰⁰ x (36/37)^36,000)
= log 37,000 - log 1 + log 36,999 - log 2 + ... + log 36,001 - log 1000 + 36,000 log 36 - 37,000 log 37

(37,000)C(1000) x (1/37)¹⁰⁰⁰ x (36/37)^36,000 = 10 to the power of (log 37,000 - log 1 + log 36,999 - log 2 + ... + log 36,001 - log 1000 + 36,000 log 36 - 37,000 log 37) = about 1 / 78.19456.

�It's not that hard; I get 1 in 78.2.
Here's how:
The probability of getting 1000, say, zeroes in 37,000 spins of a single-zero wheel is (37,000)C(1000) x (1/37)1000 x (36/37)36,000�

how�s trix? you multiplied BDF by 1000 as if 1000 successes were added as OR. based on your logic its HARDER to get 100 successes than 1000.

AND THERE AINT NO C(1000) MUST BE SUM LIKE C(1000, K) THE FORMULA IN SANE MATHS IS ONLY ONE

BDF = C(N, M) * p^M * (1 � p)^(N � M)
Notice C(N, M)

ThatDonGuy

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January 27th, 2020 at 5:01:16 PM permalink

Quote: weezrDASvegas
�It's not that hard; I get 1 in 78.2.
BDF = C(N, M) * p^M * (1 � p)^(N � M)
Notice C(N, M)

I use (N)C(M) for C(N,M). Others use Combin(N,M).

Ace2

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January 27th, 2020 at 5:05:34 PM permalink

Quote: weezrDASvegas

how�s trix? you multiplied BDF by 1000 as if 1000 successes were added as OR. based on your logic its HARDER to get 100 successes than 1000

Obviously. 1000 is the expected (and most probable) value. 100 is 900/31 = 29 standard deviations out.

It�s all about making that GTA

weezrDASvegas

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January 27th, 2020 at 5:05:34 PM permalink

Quote: ThatDonGuy
It's not that hard; I get 1 in 78.2.

Here's how:
The probability of getting 1000, say, zeroes in 37,000 spins of a single-zero wheel is (37,000)C(1000) x (1/37)¹⁰⁰⁰ x (36/37)^36,000
Most methods of calculating this would result in arithmetic overflows, but if you use logarithms and a spreadsheet, you can do it.

(37,000)C(1000) = 37,000 / 1 x 36,999 / 2 x 36,998 / 3 x ... x 36,002 / 999 x 36,001 / 1000
log ((37,000)C(1000)) = log 37,000 - log 1 + log 36,999 - log 2 + ... + log 36,001 - log 1000

(1/37)¹⁰⁰⁰ x (36/37)^36,000 = 36^36,000 / 37^37,000
log ((1/37)¹⁰⁰⁰ x (36/37)^36,000) = 36,000 log 36 - 37,000 log 37

log ((37,000)C(1000) x (1/37)¹⁰⁰⁰ x (36/37)^36,000) = log ((37,000)C(1000)) + log (1/37)¹⁰⁰⁰ x (36/37)^36,000)
= log 37,000 - log 1 + log 36,999 - log 2 + ... + log 36,001 - log 1000 + 36,000 log 36 - 37,000 log 37

(37,000)C(1000) x (1/37)¹⁰⁰⁰ x (36/37)^36,000 = 10 to the power of (log 37,000 - log 1 + log 36,999 - log 2 + ... + log 36,001 - log 1000 + 36,000 log 36 - 37,000 log 37) = about 1 / 78.19456.

�log ((37,000)C(1000) x (1/37)1000 x (36/37)36,000) = log ((37,000)C(1000)) + log (1/37)1000 x (36/37)36,000)
= log 37,000 - log 1 + log 36,999 - log 2 + ... + log 36,001 - log 1000 + 36,000 log 36 - 37,000 log 37

(37,000)C(1000) x (1/37)1000 x (36/37)36,000 = 10 to the power of (log 37,000 - log 1 + log 36,999 - log 2 + ... + log 36,001 - log 1000 + 36,000 log 36 - 37,000 log 37) = about 1 / 78.19456.�
Boy, oh, boy!!!

REPEAT
THE FORMULA IN SANE MATHS IS ONLY ONE

BDF = C(N, M) * p^M * (1 � p)^(N � M)

There aint nothing else around this formula for M SUCCESSES IN N TRIALS, where M<=N

weezrDASvegas

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January 27th, 2020 at 5:18:25 PM permalink

Quote: Ace2
Obviously. 1000 is the expected (and most probable) value. 100 is 900/31 = 29 standard deviations out.

�Obviously. 1000 is the expected (and most probable) value. 100 is 900/31 = 29 standard deviations out.�
is the most brilliant madness case in any psychiatric textbook!!!
29 STANDARD DEVIATIONS OUT!!!
THEY SETTLED FOR JUST 3 STANDARD DEVIATIONS OUT AS THEY COVER 99.7% CASES!!! HOW MANY INSANE CASES WOULD 29 STANDARD DEVIATIONS OUT COVER???

exactly 500 successes in 1000 trials: 2.5% (you might figure 50%) is NOT �the expected (and most probable) value�. The EXPECTED value is NOT the most �probable value� in the largest majority of cases.

ThatDonGuy

Threads: 122
Posts: 6677

Joined: Jun 22, 2011

January 27th, 2020 at 5:46:02 PM permalink

Quote: weezrDASvegas
Quote: ThatDonGuy
It's not that hard; I get 1 in 78.2.

Here's how:
The probability of getting 1000, say, zeroes in 37,000 spins of a single-zero wheel is (37,000)C(1000) x (1/37)¹⁰⁰⁰ x (36/37)^36,000
Most methods of calculating this would result in arithmetic overflows, but if you use logarithms and a spreadsheet, you can do it.

(37,000)C(1000) = 37,000 / 1 x 36,999 / 2 x 36,998 / 3 x ... x 36,002 / 999 x 36,001 / 1000
log ((37,000)C(1000)) = log 37,000 - log 1 + log 36,999 - log 2 + ... + log 36,001 - log 1000

(1/37)¹⁰⁰⁰ x (36/37)^36,000 = 36^36,000 / 37^37,000
log ((1/37)¹⁰⁰⁰ x (36/37)^36,000) = 36,000 log 36 - 37,000 log 37

log ((37,000)C(1000) x (1/37)¹⁰⁰⁰ x (36/37)^36,000) = log ((37,000)C(1000)) + log (1/37)¹⁰⁰⁰ x (36/37)^36,000)
= log 37,000 - log 1 + log 36,999 - log 2 + ... + log 36,001 - log 1000 + 36,000 log 36 - 37,000 log 37

(37,000)C(1000) x (1/37)¹⁰⁰⁰ x (36/37)^36,000 = 10 to the power of (log 37,000 - log 1 + log 36,999 - log 2 + ... + log 36,001 - log 1000 + 36,000 log 36 - 37,000 log 37) = about 1 / 78.19456.

�log ((37,000)C(1000) x (1/37)1000 x (36/37)36,000) = log ((37,000)C(1000)) + log (1/37)1000 x (36/37)36,000)
= log 37,000 - log 1 + log 36,999 - log 2 + ... + log 36,001 - log 1000 + 36,000 log 36 - 37,000 log 37

(37,000)C(1000) x (1/37)1000 x (36/37)36,000 = 10 to the power of (log 37,000 - log 1 + log 36,999 - log 2 + ... + log 36,001 - log 1000 + 36,000 log 36 - 37,000 log 37) = about 1 / 78.19456.�
Boy, oh, boy!!!

REPEAT
THE FORMULA IN SANE MATHS IS ONLY ONE

BDF = C(N, M) * p^M * (1 � p)^(N � M)

There aint nothing else around this formula for M SUCCESSES IN N TRIALS, where M<=N

Correct - and that's what I used,
C(37,000, 1000) * (1/37)^1000 * (36/37)^36,000 = about 1 / 78.19456.
However, if you try calculating this, you get some incredibly large numbers - for example:

C(37,000, 1000) =    479,276,699,178,809
,649,854,007,516,573,731,742,327,273,069
,805,016,086,657,405,455,109,799,606,702
,488,074,316,078,886,738,673,405,423,536
,935,995,180,640,134,170,351,203,927,583
,441,073,501,450,606,034,739,281,380,081
,266,971,643,546,937,157,336,662,888,922
,253,691,906,080,498,872,891,827,810,260
,123,627,597,442,890,261,235,017,526,349
,206,317,513,740,605,712,640,017,265,142
,974,688,761,487,034,690,463,696,780,162
,215,085,889,685,494,249,490,525,236,409
,469,240,814,649,833,608,046,768,129,786
,581,489,455,386,273,747,686,446,966,729
,405,118,683,652,656,515,783,092,956,219
,134,045,074,789,599,756,927,735,827,596
,658,822,553,856,917,516,397,236,435,813
,161,723,188,024,710,387,951,880,112,301
,158,825,892,566,463,810,963,013,768,882
,817,406,866,641,260,587,584,829,999,008
,147,384,380,458,874,009,596,572,030,879
,848,117,282,525,969,342,809,054,946,839
,342,858,681,545,894,890,490,336,636,103
,689,016,433,539,011,047,886,984,785,468
,380,720,407,098,050,506,787,090,587,675
,922,007,973,537,988,719,106,628,037,637
,201,188,379,455,839,387,495,776,823,185
,949,485,546,344,041,897,490,449,177,307
,306,200,622,994,704,372,960,416,193,336
,688,308,713,514,327,058,685,135,578,804
,394,060,159,144,923,559,645,007,689,684
,251,222,486,397,584,028,502,937,082,204
,358,533,104,641,877,406,718,240,282,261
,782,869,775,064,983,145,093,871,815,047
,611,226,716,711,985,847,297,826,933,578
,822,811,723,698,508,244,220,268,746,362
,471,556,340,712,370,272,754,537,463,366
,470,328,884,897,135,476,737,821,874,244
,866,467,383,847,786,965,458,952,998,588
,646,202,234,696,643,914,331,164,731,120
,696,118,602,946,955,042,436,415,360,583
,800,119,156,026,077,108,210,288,200,171
,543,780,460,665,972,025,328,483,787,834
,834,326,609,687,380,472,280,261,337,876
,258,947,467,008,777,949,621,986,484,591
,629,806,072,515,626,901,321,190,886,205
,758,970,285,393,041,086,834,041,780,080
,097,257,762,255,249,024,777,235,192,639
,390,351,457,284,466,347,596,327,472,028
,526,176,040,029,776,609,721,789,662,742
,918,233,956,273,583,373,632,927,934,549
,338,501,441,407,809,662,581,088,983,489
,387,476,400,674,188,551,714,927,652,671
,236,973,901,796,994,054,803,975,272,026
,083,124,171,733,928,272,977,188,321,254
,479,149,728,028,229,308,027,858,103,509
,046,658,217,579,332,379,673,689,007,685
,023,992,631,412,835,356,783,313,694,401
,502,082,353,166,957,744,010,576,726,927
,867,927,846,209,737,291,572,878,147,601
,030,873,362,980,407,225,271,549,165,836
,099,653,929,007,468,378,098,599,877,215
,417,732,947,321,440,475,756,911,637,413
,002,847,727,410,003,441,734,525,421,999
,551,574,325,706,603,163,072,805,655,372
,445,389,579,976,492,590,483,756,353,780
,275,903,959,095,519,952,117,190,925,440

That's a 1995-digit number

However, if you note a few things, it makes calculating it simpler:
10^(log N) = N
log (A * B) = log A + log B
log (A^B) = B log A

Let P be the value we are trying to calculate
P = C(37,000, 1000) * (1/37)^1000 * (36/37)^36,000
As shown in that spoiler box, C(37,000, 1000) = about 4.79277 * 10^1994
(1/37)^1000 = 1 / (37^1000), and (36/37)^36,000 = (36^36,000) / (37^36,000)
(1/37)^1000 * (36/37)^36,000 = (36^36,000) / (37^37,000)
So P = C(37,000, 1000) * (36^36,000) / (37^37,000)

log P = log (C(37,000, 1000) * (36^36,000) / (37^37,000))
= log (4.79277 * 10^1994) + log (36^36,000) - log (37^37,000)
= log 4.79277 + log (10^1994) + log (36^36,000) - log (37^37,000)
= 0.6806 + 1994 + 36,000 log (36) - 37,000 log (37)
= -1.8931763

P = 10^(log P) = 10^(-1.8931763) = about 1 / 78.1945.
Got it?

Also, some quick computing shows that 10^1058 is approximately the probability of zero coming up 3834 times in 37,000 spins.

Last edited by: ThatDonGuy on Jan 27, 2020

GeoDawg

GeoDawg

Threads: 1
Posts: 7

Joined: Jan 18, 2020

January 27th, 2020 at 8:46:04 PM permalink

Quote: ThatDonGuy
Quote: weezrDASvegas
Quote: ThatDonGuy
It's not that hard; I get 1 in 78.2.

Here's how:
The probability of getting 1000, say, zeroes in 37,000 spins of a single-zero wheel is (37,000)C(1000) x (1/37)¹⁰⁰⁰ x (36/37)^36,000
Most methods of calculating this would result in arithmetic overflows, but if you use logarithms and a spreadsheet, you can do it.

(37,000)C(1000) = 37,000 / 1 x 36,999 / 2 x 36,998 / 3 x ... x 36,002 / 999 x 36,001 / 1000
log ((37,000)C(1000)) = log 37,000 - log 1 + log 36,999 - log 2 + ... + log 36,001 - log 1000

(1/37)¹⁰⁰⁰ x (36/37)^36,000 = 36^36,000 / 37^37,000
log ((1/37)¹⁰⁰⁰ x (36/37)^36,000) = 36,000 log 36 - 37,000 log 37

log ((37,000)C(1000) x (1/37)¹⁰⁰⁰ x (36/37)^36,000) = log ((37,000)C(1000)) + log (1/37)¹⁰⁰⁰ x (36/37)^36,000)
= log 37,000 - log 1 + log 36,999 - log 2 + ... + log 36,001 - log 1000 + 36,000 log 36 - 37,000 log 37

(37,000)C(1000) x (1/37)¹⁰⁰⁰ x (36/37)^36,000 = 10 to the power of (log 37,000 - log 1 + log 36,999 - log 2 + ... + log 36,001 - log 1000 + 36,000 log 36 - 37,000 log 37) = about 1 / 78.19456.

�log ((37,000)C(1000) x (1/37)1000 x (36/37)36,000) = log ((37,000)C(1000)) + log (1/37)1000 x (36/37)36,000)
= log 37,000 - log 1 + log 36,999 - log 2 + ... + log 36,001 - log 1000 + 36,000 log 36 - 37,000 log 37

(37,000)C(1000) x (1/37)1000 x (36/37)36,000 = 10 to the power of (log 37,000 - log 1 + log 36,999 - log 2 + ... + log 36,001 - log 1000 + 36,000 log 36 - 37,000 log 37) = about 1 / 78.19456.�
Boy, oh, boy!!!

REPEAT
THE FORMULA IN SANE MATHS IS ONLY ONE

BDF = C(N, M) * p^M * (1 � p)^(N � M)

There aint nothing else around this formula for M SUCCESSES IN N TRIALS, where M<=N
Correct - and that's what I used,
C(37,000, 1000) * (1/37)^1000 * (36/37)^36,000 = about 1 / 78.19456.
However, if you try calculating this, you get some incredibly large numbers - for example:
C(37,000, 1000) =    479,276,699,178,809
,649,854,007,516,573,731,742,327,273,069
,805,016,086,657,405,455,109,799,606,702
,488,074,316,078,886,738,673,405,423,536
,935,995,180,640,134,170,351,203,927,583
,441,073,501,450,606,034,739,281,380,081
,266,971,643,546,937,157,336,662,888,922
,253,691,906,080,498,872,891,827,810,260
,123,627,597,442,890,261,235,017,526,349
,206,317,513,740,605,712,640,017,265,142
,974,688,761,487,034,690,463,696,780,162
,215,085,889,685,494,249,490,525,236,409
,469,240,814,649,833,608,046,768,129,786
,581,489,455,386,273,747,686,446,966,729
,405,118,683,652,656,515,783,092,956,219
,134,045,074,789,599,756,927,735,827,596
,658,822,553,856,917,516,397,236,435,813
,161,723,188,024,710,387,951,880,112,301
,158,825,892,566,463,810,963,013,768,882
,817,406,866,641,260,587,584,829,999,008
,147,384,380,458,874,009,596,572,030,879
,848,117,282,525,969,342,809,054,946,839
,342,858,681,545,894,890,490,336,636,103
,689,016,433,539,011,047,886,984,785,468
,380,720,407,098,050,506,787,090,587,675
,922,007,973,537,988,719,106,628,037,637
,201,188,379,455,839,387,495,776,823,185
,949,485,546,344,041,897,490,449,177,307
,306,200,622,994,704,372,960,416,193,336
,688,308,713,514,327,058,685,135,578,804
,394,060,159,144,923,559,645,007,689,684
,251,222,486,397,584,028,502,937,082,204
,358,533,104,641,877,406,718,240,282,261
,782,869,775,064,983,145,093,871,815,047
,611,226,716,711,985,847,297,826,933,578
,822,811,723,698,508,244,220,268,746,362
,471,556,340,712,370,272,754,537,463,366
,470,328,884,897,135,476,737,821,874,244
,866,467,383,847,786,965,458,952,998,588
,646,202,234,696,643,914,331,164,731,120
,696,118,602,946,955,042,436,415,360,583
,800,119,156,026,077,108,210,288,200,171
,543,780,460,665,972,025,328,483,787,834
,834,326,609,687,380,472,280,261,337,876
,258,947,467,008,777,949,621,986,484,591
,629,806,072,515,626,901,321,190,886,205
,758,970,285,393,041,086,834,041,780,080
,097,257,762,255,249,024,777,235,192,639
,390,351,457,284,466,347,596,327,472,028
,526,176,040,029,776,609,721,789,662,742
,918,233,956,273,583,373,632,927,934,549
,338,501,441,407,809,662,581,088,983,489
,387,476,400,674,188,551,714,927,652,671
,236,973,901,796,994,054,803,975,272,026
,083,124,171,733,928,272,977,188,321,254
,479,149,728,028,229,308,027,858,103,509
,046,658,217,579,332,379,673,689,007,685
,023,992,631,412,835,356,783,313,694,401
,502,082,353,166,957,744,010,576,726,927
,867,927,846,209,737,291,572,878,147,601
,030,873,362,980,407,225,271,549,165,836
,099,653,929,007,468,378,098,599,877,215
,417,732,947,321,440,475,756,911,637,413
,002,847,727,410,003,441,734,525,421,999
,551,574,325,706,603,163,072,805,655,372
,445,389,579,976,492,590,483,756,353,780
,275,903,959,095,519,952,117,190,925,440
That's a 1995-digit number
However, if you note a few things, it makes calculating it simpler:
10^(log N) = N
log (A * B) = log A + log B
log (A^B) = B log A

Let P be the value we are trying to calculate
P = C(37,000, 1000) * (1/37)^1000 * (36/37)^36,000
As shown in that spoiler box, C(37,000, 1000) = about 4.79277 * 10^1994
(1/37)^1000 = 1 / (37^1000), and (36/37)^36,000 = (36^36,000) / (37^36,000)
(1/37)^1000 * (36/37)^36,000 = (36^36,000) / (37^37,000)
So P = C(37,000, 1000) * (36^36,000) / (37^37,000)

log P = log (C(37,000, 1000) * (36^36,000) / (37^37,000))
= log (4.79277 * 10^1994) + log (36^36,000) - log (37^37,000)
= log 4.79277 + log (10^1994) + log (36^36,000) - log (37^37,000)
= 0.6806 + 1994 + 36,000 log (36) - 37,000 log (37)
= -1.8931763

P = 10^(log P) = 10^(-1.8931763) = about 1 / 78.1945.
Got it?

Also, some quick computing shows that 10^1058 is approximately the probability of zero coming up 3834 times in 37,000 spins.

Copy and paste the link^

ThatDonGuy

Threads: 122
Posts: 6677

Joined: Jun 22, 2011

January 28th, 2020 at 4:37:43 PM permalink

Quote: GeoDawg
Copy and paste the link^

For some strange reason, the link didn't show up until I replied to the message.

Is there anything in particular I should be looking at in that paper?

Here are the probabilities (expressed as "1 in X") of getting exactly N zeroes in 37,000 spins, for N = 0, 10, 20, 30, ..., 9980, 9990:
(I was going to post numbers up to 37,000, but the post was too long for the board software to handle):

	0	10	20	30	40	50	60	70	80	90
0	1.8675 x 10^440	5.1589 x 10^416	2.6401 x 10^398	2.2031 x 10^382	5.2011 x 10^367	1.4919 x 10^354	3.1497 x 10^341	3.5082 x 10^329	1.6261 x 10^318	2.6261 x 10^307
100	1.2867 x 10^297	1.7127 x 10^287	5.6577 x 10^277	4.3012 x 10^268	7.0604 x 10^259	2.3692 x 10^251	1.5501 x 10^243	1.8969 x 10^235	4.1857 x 10^227	1.6121 x 10^220
200	1.0527 x 10^213	1.1352 x 10^206	1.9743 x 10^199	5.4197 x 10^192	2.3024 x 10^186	1.4866 x 10^180	1.4348 x 10^174	2.0388 x 10^168	4.2044 x 10^162	1.2418 x 10^157
300	5.1899 x 10^151	3.0337 x 10^146	2.4539 x 10^141	2.7194 x 10^136	4.0896 x 10^131	8.2728 x 10^126	2.2321 x 10^122	7.9702 x 10^117	3.7379 x 10^113	2.2862 x 10^109
400	1.8115 x 10^105	1.8475 x 10^101	2.4106 x 10^97	4.0008 x 10^93	8.3994 x 10^89	2.2188 x 10^86	7.3386 x 10^82	3.0241 x 10^79	1.5455 x 10^76	9.7535 x 10^72
500	7.5678 x 10^69	7.1902 x 10^66	8.3326 x 10^63	1.1734 x 10^61	2.0007 x 10^58	4.1160 x 10^55	1.0182 x 10^53	3.0192 x 10^50	1.0696 x 10^48	4.5148 x 10^45
600	2.2634 x 10^43	1.3440 x 10^41	9.4271 x 10^38	7.7900 x 10^36	7.5645 x 10^34	8.6104 x 10^32	1.1461 x 10^31	1.7798 x 10^29	3.2174 x 10^27	6.7553 x 10^25
700	1.6439 x 10^24	4.6271 x 10^22	1.5033 x 10^21	5.6272 x 10^19	2.4220 x 10^18	1.1964 x 10^17	6.7718 x 10^15	4.3834 x 10^14	3.2395 x 10^13	2.7289 x 10^12
800	2.6160 x 10^11	2.8494 x 10^10	3.5208 x 10^9	4.9280 x 10^8	7.8017 x 10^7	1.3950 x 10^7	2.8134 x 10^6	6.3910 x 10^5	1.6330 x 10^5	46875.81244
900	15096.41253	5447.92164	2200.34465	993.42585	500.79311	281.55512	176.34582	122.91029	95.22850	81.93044
1,000	78.19454	82.70320	96.83978	125.41516	179.47268	283.52674	494.01491	948.52092	2005.08314	4662.52648
1,100	11916.40996	33445.92384	1.0300 x 10^5	3.4781 x 10^5	1.2866 x 10^6	5.2103 x 10^6	2.3079 x 10^7	1.1174 x 10^8	5.9094 x 10^8	3.4108 x 10^9
1,200	2.1472 x 10^10	1.4732 x 10^11	1.1009 x 10^12	8.9547 x 10^12	7.9223 x 10^13	7.6185 x 10^14	7.9586 x 10^15	9.0256 x 10^16	1.1104 x 10^18	1.4814 x 10^19
1,300	2.1415 x 10^20	3.3524 x 10^21	5.6803 x 10^22	1.0410 x 10^24	2.0627 x 10^25	4.4161 x 10^26	1.0209 x 10^28	2.5474 x 10^29	6.8567 x 10^30	1.9898 x 10^32
1,400	6.2223 x 10^33	2.0956 x 10^35	7.5982 x 10^36	2.9640 x 10^38	1.2435 x 10^40	5.6076 x 10^41	2.7168 x 10^43	1.4135 x 10^45	7.8945 x 10^46	4.7303 x 10^48
1,500	3.0396 x 10^50	2.0936 x 10^52	1.5451 x 10^54	1.2213 x 10^56	1.0334 x 10^58	9.3574 x 10^59	9.0628 x 10^61	9.3848 x 10^63	1.0386 x 10^66	1.2280 x 10^68
1,600	1.5505 x 10^70	2.0899 x 10^72	3.0058 x 10^74	4.6113 x 10^76	7.5432 x 10^78	1.3151 x 10^81	2.4431 x 10^83	4.8339 x 10^85	1.0183 x 10^88	2.2831 x 10^90
1,700	5.4464 x 10^92	1.3818 x 10^95	3.7274 x 10^97	1.0686 x 10^100	3.2555 x 10^102	1.0533 x 10^105	3.6187 x 10^107	1.3196 x 10^110	5.1062 x 10^112	2.0959 x 10^115
1,800	9.1233 x 10^117	4.2099 x 10^120	2.0588 x 10^123	1.0667 x 10^126	5.8539 x 10^128	3.4015 x 10^131	2.0922 x 10^134	1.3618 x 10^137	9.3775 x 10^139	6.8294 x 10^142
1,900	5.2588 x 10^145	4.2804 x 10^148	3.6817 x 10^151	3.3455 x 10^154	3.2108 x 10^157	3.2537 x 10^160	3.4807 x 10^163	3.9294 x 10^166	4.6803 x 10^169	5.8802 x 10^172
2,000	7.7906 x 10^175	1.0881 x 10^179	1.6020 x 10^182	2.4852 x 10^185	4.0616 x 10^188	6.9914 x 10^191	1.2672 x 10^195	2.4179 x 10^198	4.8559 x 10^201	1.0261 x 10^205
2,100	2.2812 x 10^208	5.3339 x 10^211	1.3114 x 10^215	3.3898 x 10^218	9.2095 x 10^221	2.6292 x 10^225	7.8861 x 10^228	2.4845 x 10^232	8.2202 x 10^235	2.8555 x 10^239
2,200	1.0412 x 10^243	3.9849 x 10^246	1.6002 x 10^250	6.7413 x 10^253	2.9787 x 10^257	1.3802 x 10^261	6.7052 x 10^264	3.4145 x 10^268	1.8223 x 10^272	1.0191 x 10^276
2,300	5.9711 x 10^279	3.6643 x 10^283	2.3549 x 10^287	1.5846 x 10^291	1.1163 x 10^295	8.2308 x 10^298	6.3508 x 10^302	5.1270 x 10^306	4.3298 x 10^310	3.8246 x 10^314
2,400	3.5328 x 10^318	3.4119 x 10^322	3.4446 x 10^326	3.6349 x 10^330	4.0084 x 10^334	4.6185 x 10^338	5.5591 x 10^342	6.9891 x 10^346	9.1764 x 10^350	1.2580 x 10^355
2,500	1.8005 x 10^359	2.6899 x 10^363	4.1942 x 10^367	6.8240 x 10^371	1.1583 x 10^376	2.0512 x 10^380	3.7885 x 10^384	7.2971 x 10^388	1.4655 x 10^393	3.0684 x 10^397
2,600	6.6968 x 10^401	1.5233 x 10^406	3.6108 x 10^410	8.9177 x 10^414	2.2944 x 10^419	6.1492 x 10^423	1.7163 x 10^428	4.9886 x 10^432	1.5096 x 10^437	4.7561 x 10^441
2,700	1.5596 x 10^446	5.3230 x 10^450	1.8905 x 10^455	6.9859 x 10^459	2.6856 x 10^464	1.0739 x 10^469	4.4665 x 10^473	1.9317 x 10^478	8.6875 x 10^482	4.0618 x 10^487
2,800	1.9741 x 10^492	9.9728 x 10^496	5.2357 x 10^501	2.8563 x 10^506	1.6189 x 10^511	9.5334 x 10^515	5.8311 x 10^520	3.7044 x 10^525	2.4439 x 10^530	1.6741 x 10^535
2,900	1.1907 x 10^540	8.7918 x 10^544	6.7380 x 10^549	5.3596 x 10^554	4.4241 x 10^559	3.7894 x 10^564	3.3675 x 10^569	3.1044 x 10^574	2.9687 x 10^579	2.9443 x 10^584
3,000	3.0284 x 10^589	3.2299 x 10^594	3.5716 x 10^599	4.0945 x 10^604	4.8658 x 10^609	5.9932 x 10^614	7.6504 x 10^619	1.0120 x 10^625	1.3870 x 10^630	1.9696 x 10^635
3,100	2.8975 x 10^640	4.4151 x 10^645	6.9679 x 10^650	1.1388 x 10^656	1.9274 x 10^661	3.3776 x 10^666	6.1278 x 10^671	1.1508 x 10^677	2.2373 x 10^682	4.5016 x 10^687
3,200	9.3736 x 10^692	2.0197 x 10^698	4.5030 x 10^703	1.0386 x 10^709	2.4784 x 10^714	6.1175 x 10^719	1.5617 x 10^725	4.1235 x 10^730	1.1258 x 10^736	3.1785 x 10^741
3,300	9.2780 x 10^746	2.7998 x 10^752	8.7340 x 10^757	2.8162 x 10^763	9.3853 x 10^768	3.2323 x 10^774	1.1504 x 10^780	4.2304 x 10^785	1.6073 x 10^791	6.3090 x 10^796
3,400	2.5581 x 10^802	1.0713 x 10^808	4.6343 x 10^813	2.0702 x 10^819	9.5503 x 10^824	4.5491 x 10^830	2.2372 x 10^836	1.1359 x 10^842	5.9538 x 10^847	3.2211 x 10^853
3,500	1.7987 x 10^859	1.0366 x 10^865	6.1653 x 10^870	3.7836 x 10^876	2.3959 x 10^882	1.5653 x 10^888	1.0549 x 10^894	7.3350 x 10^899	5.2603 x 10^905	3.8909 x 10^911
3,600	2.9681 x 10^917	2.3350 x 10^923	1.8941 x 10^929	1.5843 x 10^935	1.3662 x 10^941	1.2146 x 10^947	1.1131 x 10^953	1.0516 x 10^959	1.0239 x 10^965	1.0275 x 10^971
3,700	1.0626 x 10^977	1.1324 x 10^983	1.2436 x 10^989	1.4070 x 10^995	1.6401 x 10^1001	1.9695 x 10^1007	2.4363 x 10^1013	3.1043 x 10^1019	4.0739 x 10^1025	5.5063 x 10^1031
3,800	7.6644 x 10^1037	1.0985 x 10^1044	1.6213 x 10^1050	2.4638 x 10^1056	3.8547 x 10^1062	6.2085 x 10^1068	1.0293 x 10^1075	1.7567 x 10^1081	3.0860 x 10^1087	5.5792 x 10^1093
3,900	1.0380 x 10^1100	1.9876 x 10^1106	3.9160 x 10^1112	7.9388 x 10^1118	1.6558 x 10^1125	3.5533 x 10^1131	7.8442 x 10^1137	1.7813 x 10^1144	4.1609 x 10^1150	9.9969 x 10^1156
4,000	2.4702 x 10^1163	6.2774 x 10^1169	1.6404 x 10^1176	4.4084 x 10^1182	1.2181 x 10^1189	3.4605 x 10^1195	1.0107 x 10^1202	3.0351 x 10^1208	9.3688 x 10^1214	2.9727 x 10^1221
4,100	9.6954 x 10^1227	3.2500 x 10^1234	1.1196 x 10^1241	3.9642 x 10^1247	1.4423 x 10^1254	5.3922 x 10^1260	2.0714 x 10^1267	8.1757 x 10^1273	3.3153 x 10^1280	1.3811 x 10^1287
4,200	5.9105 x 10^1293	2.5982 x 10^1300	1.1732 x 10^1307	5.4411 x 10^1313	2.5917 x 10^1320	1.2678 x 10^1327	6.3691 x 10^1333	3.2855 x 10^1340	1.7403 x 10^1347	9.4655 x 10^1353
4,300	5.2856 x 10^1360	3.0302 x 10^1367	1.7834 x 10^1374	1.0775 x 10^1381	6.6827 x 10^1387	4.2541 x 10^1394	2.7796 x 10^1401	1.8639 x 10^1408	1.2828 x 10^1415	9.0604 x 10^1421
4,400	6.5666 x 10^1428	4.8836 x 10^1435	3.7267 x 10^1442	2.9178 x 10^1449	2.3438 x 10^1456	1.9316 x 10^1463	1.6330 x 10^1470	1.4162 x 10^1477	1.2599 x 10^1484	1.1496 x 10^1491
4,500	1.0760 x 10^1498	1.0328 x 10^1505	1.0167 x 10^1512	1.0264 x 10^1519	1.0626 x 10^1526	1.1281 x 10^1533	1.2280 x 10^1540	1.3705 x 10^1547	1.5683 x 10^1554	1.8399 x 10^1561
4,600	2.2129 x 10^1568	2.7285 x 10^1575	3.4485 x 10^1582	4.4676 x 10^1589	5.9325 x 10^1596	8.0744 x 10^1603	1.1263 x 10^1611	1.6101 x 10^1618	2.3589 x 10^1625	3.5415 x 10^1632
4,700	5.4484 x 10^1639	8.5889 x 10^1646	1.3872 x 10^1654	2.2958 x 10^1661	3.8925 x 10^1668	6.7614 x 10^1675	1.2031 x 10^1683	2.1933 x 10^1690	4.0955 x 10^1697	7.8336 x 10^1704
4,800	1.5347 x 10^1712	3.0795 x 10^1719	6.3288 x 10^1726	1.3320 x 10^1734	2.8711 x 10^1741	6.3373 x 10^1748	1.4324 x 10^1756	3.3152 x 10^1763	7.8566 x 10^1770	1.9063 x 10^1778
4,900	4.7359 x 10^1785	1.2045 x 10^1793	3.1364 x 10^1800	8.3603 x 10^1807	2.2812 x 10^1815	6.3721 x 10^1822	1.8218 x 10^1830	5.3315 x 10^1837	1.5969 x 10^1845	4.8954 x 10^1852
5,000	1.5358 x 10^1860	4.9313 x 10^1867	1.6203 x 10^1875	5.4481 x 10^1882	1.8744 x 10^1890	6.5992 x 10^1897	2.3771 x 10^1905	8.7613 x 10^1912	3.3037 x 10^1920	1.2745 x 10^1928
5,100	5.0302 x 10^1935	2.0309 x 10^1943	8.3883 x 10^1950	3.5439 x 10^1958	1.5315 x 10^1966	6.7700 x 10^1973	3.0608 x 10^1981	1.4153 x 10^1989	6.6937 x 10^1996	3.2375 x 10^2004
5,200	1.6013 x 10^2012	8.0999 x 10^2019	4.1896 x 10^2027	2.2159 x 10^2035	1.1984 x 10^2043	6.6268 x 10^2050	3.7467 x 10^2058	2.1657 x 10^2066	1.2799 x 10^2074	7.7332 x 10^2081
5,300	4.7765 x 10^2089	3.0159 x 10^2097	1.9466 x 10^2105	1.2843 x 10^2113	8.6613 x 10^2120	5.9703 x 10^2128	4.2063 x 10^2136	3.0289 x 10^2144	2.2290 x 10^2152	1.6765 x 10^2160
5,400	1.2886 x 10^2168	1.0121 x 10^2176	8.1243 x 10^2183	6.6635 x 10^2191	5.5847 x 10^2199	4.7824 x 10^2207	4.1845 x 10^2215	3.7408 x 10^2223	3.4167 x 10^2231	3.1883 x 10^2239
5,500	3.0394 x 10^2247	2.9600 x 10^2255	2.9448 x 10^2263	2.9928 x 10^2271	3.1069 x 10^2279	3.2945 x 10^2287	3.5683 x 10^2295	3.9475 x 10^2303	4.4603 x 10^2311	5.1472 x 10^2319
5,600	6.0663 x 10^2327	7.3017 x 10^2335	8.9751 x 10^2343	1.1266 x 10^2352	1.4441 x 10^2360	1.8902 x 10^2368	2.5263 x 10^2376	3.4477 x 10^2384	4.8041 x 10^2392	6.8349 x 10^2400
5,700	9.9282 x 10^2408	1.4723 x 10^2417	2.2292 x 10^2425	3.4456 x 10^2433	5.4369 x 10^2441	8.7576 x 10^2449	1.4400 x 10^2458	2.4170 x 10^2466	4.1410 x 10^2474	7.2416 x 10^2482
5,800	1.2925 x 10^2491	2.3548 x 10^2499	4.3785 x 10^2507	8.3090 x 10^2515	1.6092 x 10^2524	3.1805 x 10^2532	6.4153 x 10^2540	1.3204 x 10^2549	2.7736 x 10^2557	5.9447 x 10^2565
5,900	1.3001 x 10^2574	2.9014 x 10^2582	6.6064 x 10^2590	1.5348 x 10^2599	3.6381 x 10^2607	8.7983 x 10^2615	2.1708 x 10^2624	5.4642 x 10^2632	1.4031 x 10^2641	3.6757 x 10^2649
6,000	9.8228 x 10^2657	2.6777 x 10^2666	7.4460 x 10^2674	2.1120 x 10^2683	6.1104 x 10^2691	1.8031 x 10^2700	5.4274 x 10^2708	1.6661 x 10^2717	5.2166 x 10^2725	1.6657 x 10^2734
6,100	5.4246 x 10^2742	1.8015 x 10^2751	6.1017 x 10^2759	2.1074 x 10^2768	7.4224 x 10^2776	2.6657 x 10^2785	9.7624 x 10^2793	3.6454 x 10^2802	1.3880 x 10^2811	5.3886 x 10^2819
6,200	2.1329 x 10^2828	8.6080 x 10^2836	3.5418 x 10^2845	1.4857 x 10^2854	6.3539 x 10^2862	2.7701 x 10^2871	1.2312 x 10^2880	5.5785 x 10^2888	2.5765 x 10^2897	1.2130 x 10^2906
6,300	5.8216 x 10^2914	2.8478 x 10^2923	1.4200 x 10^2932	7.2168 x 10^2940	3.7383 x 10^2949	1.9736 x 10^2958	1.0620 x 10^2967	5.8241 x 10^2975	3.2551 x 10^2984	1.8540 x 10^2993
6,400	1.0762 x 10^3002	6.3662 x 10^3010	3.8375 x 10^3019	2.3573 x 10^3028	1.4755 x 10^3037	9.4112 x 10^3045	6.1164 x 10^3054	4.0503 x 10^3063	2.7328 x 10^3072	1.8787 x 10^3081
6,500	1.3159 x 10^3090	9.3911 x 10^3098	6.8279 x 10^3107	5.0575 x 10^3116	3.8165 x 10^3125	2.9340 x 10^3134	2.2978 x 10^3143	1.8332 x 10^3152	1.4898 x 10^3161	1.2334 x 10^3170
6,600	1.0401 x 10^3179	8.9348 x 10^3187	7.8175 x 10^3196	6.9670 x 10^3205	6.3242 x 10^3214	5.8470 x 10^3223	5.5058 x 10^3232	5.2803 x 10^3241	5.1575 x 10^3250	5.1305 x 10^3259
6,700	5.1975 x 10^3268	5.3623 x 10^3277	5.6340 x 10^3286	6.0280 x 10^3295	6.5677 x 10^3304	7.2868 x 10^3313	8.2325 x 10^3322	9.4707 x 10^3331	1.1094 x 10^3341	1.3232 x 10^3350
6,800	1.6069 x 10^3359	1.9870 x 10^3368	2.5016 x 10^3377	3.2067 x 10^3386	4.1848 x 10^3395	5.5602 x 10^3404	7.5211 x 10^3413	1.0357 x 10^3423	1.4520 x 10^3432	2.0722 x 10^3441
6,900	3.0107 x 10^3450	4.4527 x 10^3459	6.7037 x 10^3468	1.0273 x 10^3478	1.6026 x 10^3487	2.5448 x 10^3496	4.1132 x 10^3505	6.7667 x 10^3514	1.1330 x 10^3524	1.9310 x 10^3533
7,000	3.3496 x 10^3542	5.9136 x 10^3551	1.0625 x 10^3561	1.9430 x 10^3570	3.6161 x 10^3579	6.8489 x 10^3588	1.3201 x 10^3598	2.5894 x 10^3607	5.1687 x 10^3616	1.0499 x 10^3626
7,100	2.1701 x 10^3635	4.5646 x 10^3644	9.7696 x 10^3653	2.1276 x 10^3663	4.7149 x 10^3672	1.0631 x 10^3682	2.4390 x 10^3691	5.6934 x 10^3700	1.3522 x 10^3710	3.2675 x 10^3719
7,200	8.0332 x 10^3728	2.0093 x 10^3738	5.1131 x 10^3747	1.3237 x 10^3757	3.4864 x 10^3766	9.3414 x 10^3775	2.5462 x 10^3785	7.0603 x 10^3794	1.9915 x 10^3804	5.7144 x 10^3813
7,300	1.6679 x 10^3823	4.9522 x 10^3832	1.4956 x 10^3842	4.5945 x 10^3851	1.4356 x 10^3861	4.5627 x 10^3870	1.4749 x 10^3880	4.8496 x 10^3889	1.6217 x 10^3899	5.5160 x 10^3908
7,400	1.9081 x 10^3918	6.7130 x 10^3927	2.4019 x 10^3937	8.7401 x 10^3946	3.2343 x 10^3956	1.2172 x 10^3966	4.6585 x 10^3975	1.8131 x 10^3985	7.1759 x 10^3994	2.8880 x 10^4004
7,500	1.1819 x 10^4014	4.9189 x 10^4023	2.0815 x 10^4033	8.9569 x 10^4042	3.9189 x 10^4052	1.7434 x 10^4062	7.8863 x 10^4071	3.6271 x 10^4081	1.6961 x 10^4091	8.0642 x 10^4100
7,600	3.8982 x 10^4110	1.9158 x 10^4120	9.5728 x 10^4129	4.8628 x 10^4139	2.5114 x 10^4149	1.3185 x 10^4159	7.0380 x 10^4168	3.8189 x 10^4178	2.1066 x 10^4188	1.1812 x 10^4198
7,700	6.7338 x 10^4207	3.9019 x 10^4217	2.2983 x 10^4227	1.3761 x 10^4237	8.3756 x 10^4246	5.1816 x 10^4256	3.2583 x 10^4266	2.0826 x 10^4276	1.3530 x 10^4286	8.9341 x 10^4295
7,800	5.9961 x 10^4305	4.0902 x 10^4315	2.8357 x 10^4325	1.9981 x 10^4335	1.4309 x 10^4345	1.0414 x 10^4355	7.7037 x 10^4364	5.7911 x 10^4374	4.4242 x 10^4384	3.4348 x 10^4394
7,900	2.7100 x 10^4404	2.1729 x 10^4414	1.7704 x 10^4424	1.4659 x 10^4434	1.2333 x 10^4444	1.0545 x 10^4454	9.1613 x 10^4463	8.0876 x 10^4473	7.2548 x 10^4483	6.6126 x 10^4493
8,000	6.1242 x 10^4503	5.7630 x 10^4513	5.5103 x 10^4523	5.3531 x 10^4533	5.2839 x 10^4543	5.2990 x 10^4553	5.3993 x 10^4563	5.5894 x 10^4573	5.8786 x 10^4583	6.2815 x 10^4593
8,100	6.8190 x 10^4603	7.5204 x 10^4613	8.4259 x 10^4623	9.5907 x 10^4633	1.1089 x 10^4644	1.3026 x 10^4654	1.5545 x 10^4664	1.8843 x 10^4674	2.3204 x 10^4684	2.9025 x 10^4694
8,200	3.6881 x 10^4704	4.7603 x 10^4714	6.2411 x 10^4724	8.3116 x 10^4734	1.1243 x 10^4745	1.5448 x 10^4755	2.1559 x 10^4765	3.0560 x 10^4775	4.4000 x 10^4785	6.4343 x 10^4795
8,300	9.5566 x 10^4805	1.4416 x 10^4816	2.2086 x 10^4826	3.4367 x 10^4836	5.4312 x 10^4846	8.7169 x 10^4856	1.4208 x 10^4867	2.3520 x 10^4877	3.9541 x 10^4887	6.7507 x 10^4897
8,400	1.1704 x 10^4908	2.0607 x 10^4918	3.6846 x 10^4928	6.6901 x 10^4938	1.2335 x 10^4949	2.3095 x 10^4959	4.3911 x 10^4969	8.4775 x 10^4979	1.6619 x 10^4990	3.3082 x 10^5000
8,500	6.6870 x 10^5010	1.3724 x 10^5021	2.8600 x 10^5031	6.0518 x 10^5041	1.3002 x 10^5052	2.8363 x 10^5062	6.2819 x 10^5072	1.4126 x 10^5083	3.2253 x 10^5093	7.4766 x 10^5103
8,600	1.7596 x 10^5114	4.2044 x 10^5124	1.0199 x 10^5135	2.5119 x 10^5145	6.2805 x 10^5155	1.5942 x 10^5166	4.1082 x 10^5176	1.0747 x 10^5187	2.8543 x 10^5197	7.6954 x 10^5207
8,700	2.1061 x 10^5218	5.8517 x 10^5228	1.6504 x 10^5239	4.7251 x 10^5249	1.3732 x 10^5260	4.0513 x 10^5270	1.2132 x 10^5281	3.6878 x 10^5291	1.1378 x 10^5302	3.5638 x 10^5312
8,800	1.1329 x 10^5323	3.6557 x 10^5333	1.1973 x 10^5344	3.9802 x 10^5354	1.3429 x 10^5365	4.5992 x 10^5375	1.5986 x 10^5386	5.6398 x 10^5396	2.0193 x 10^5407	7.3384 x 10^5417
8,900	2.7065 x 10^5428	1.0131 x 10^5439	3.8487 x 10^5449	1.4838 x 10^5460	5.8060 x 10^5470	2.3055 x 10^5481	9.2909 x 10^5491	3.7996 x 10^5502	1.5769 x 10^5513	6.6418 x 10^5523
9,000	2.8387 x 10^5534	1.2312 x 10^5545	5.4193 x 10^5555	2.4205 x 10^5566	1.0970 x 10^5577	5.0455 x 10^5587	2.3547 x 10^5598	1.1150 x 10^5609	5.3583 x 10^5619	2.6127 x 10^5630
9,100	1.2926 x 10^5641	6.4894 x 10^5651	3.3056 x 10^5662	1.7085 x 10^5673	8.9597 x 10^5683	4.7674 x 10^5694	2.5738 x 10^5705	1.4098 x 10^5716	7.8355 x 10^5726	4.4182 x 10^5737
9,200	2.5277 x 10^5748	1.4671 x 10^5759	8.6399 x 10^5769	5.1619 x 10^5780	3.1288 x 10^5791	1.9241 x 10^5802	1.2004 x 10^5813	7.5976 x 10^5823	4.8784 x 10^5834	3.1778 x 10^5845
9,300	2.1000 x 10^5856	1.4078 x 10^5867	9.5745 x 10^5877	6.6055 x 10^5888	4.6230 x 10^5899	3.2821 x 10^5910	2.3638 x 10^5921	1.7269 x 10^5932	1.2797 x 10^5943	9.6208 x 10^5953
9,400	7.3363 x 10^5964	5.6746 x 10^5975	4.4523 x 10^5986	3.5434 x 10^5997	2.8604 x 10^6008	2.3422 x 10^6019	1.9453 x 10^6030	1.6387 x 10^6041	1.4002 x 10^6052	1.2135 x 10^6063
9,500	1.0667 x 10^6074	9.5112 x 10^6084	8.6008 x 10^6095	7.8884 x 10^6106	7.3379 x 10^6117	6.9229 x 10^6128	6.6243 x 10^6139	6.4285 x 10^6150	6.3271 x 10^6161	6.3156 x 10^6172
9,600	6.3935 x 10^6183	6.5640 x 10^6194	6.8345 x 10^6205	7.2168 x 10^6216	7.7282 x 10^6227	8.3927 x 10^6238	9.2431 x 10^6249	1.0323 x 10^6261	1.1692 x 10^6272	1.3429 x 10^6283
9,700	1.5641 x 10^6294	1.8474 x 10^6305	2.2127 x 10^6316	2.6874 x 10^6327	3.3099 x 10^6338	4.1337 x 10^6349	5.2349 x 10^6360	6.7224 x 10^6371	8.7535 x 10^6382	1.1557 x 10^6394
9,800	1.5473 x 10^6405	2.1006 x 10^6416	2.8915 x 10^6427	4.0357 x 10^6438	5.7113 x 10^6449	8.1952 x 10^6460	1.1923 x 10^6472	1.7588 x 10^6483	2.6306 x 10^6494	3.9893 x 10^6505
9,900	6.1338 x 10^6516	9.5620 x 10^6527	1.5113 x 10^6539	2.4217 x 10^6550	3.9345 x 10^6561	6.4808 x 10^6572	1.0822 x 10^6584	1.8323 x 10^6595	3.1451 x 10^6606	5.4731 x 10^6617

ThatDonGuy

Threads: 122
Posts: 6677

Joined: Jun 22, 2011

January 28th, 2020 at 4:38:51 PM permalink

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10,000	9.6557 x 10^6628	1.7269 x 10^6640	3.1313 x 10^6651	5.7560 x 10^6662	1.0726 x 10^6674	2.0263 x 10^6685	3.8807 x 10^6696	7.5343 x 10^6707	1.4828 x 10^6719	2.9585 x 10^6730
10,100	5.9836 x 10^6741	1.2267 x 10^6753	2.5497 x 10^6764	5.3717 x 10^6775	1.1472 x 10^6787	2.4835 x 10^6798	5.4499 x 10^6809	1.2122 x 10^6821	2.7334 x 10^6832	6.2474 x 10^6843
10,200	1.4473 x 10^6855	3.3987 x 10^6866	8.0899 x 10^6877	1.9518 x 10^6889	4.7731 x 10^6900	1.1831 x 10^6912	2.9724 x 10^6923	7.5692 x 10^6934	1.9536 x 10^6946	5.1108 x 10^6957
10,300	1.3551 x 10^6969	3.6418 x 10^6980	9.9197 x 10^6991	2.7384 x 10^7003	7.6621 x 10^7014	2.1728 x 10^7026	6.2448 x 10^7037	1.8190 x 10^7049	5.3700 x 10^7060	1.6066 x 10^7072
10,400	4.8718 x 10^7083	1.4971 x 10^7095	4.6627 x 10^7106	1.4717 x 10^7118	4.7076 x 10^7129	1.5260 x 10^7141	5.0134 x 10^7152	1.6691 x 10^7164	5.6315 x 10^7175	1.9254 x 10^7187
10,500	6.6717 x 10^7198	2.3426 x 10^7210	8.3359 x 10^7221	3.0058 x 10^7233	1.0983 x 10^7245	4.0670 x 10^7256	1.5260 x 10^7268	5.8025 x 10^7279	2.2357 x 10^7291	8.7291 x 10^7302
10,600	3.4535 x 10^7314	1.3845 x 10^7326	5.6244 x 10^7337	2.3152 x 10^7349	9.6568 x 10^7360	4.0814 x 10^7372	1.7478 x 10^7384	7.5845 x 10^7395	3.3348 x 10^7407	1.4856 x 10^7419
10,700	6.7065 x 10^7430	3.0674 x 10^7442	1.4215 x 10^7454	6.6750 x 10^7465	3.1757 x 10^7477	1.5308 x 10^7489	7.4768 x 10^7500	3.6999 x 10^7512	1.8550 x 10^7524	9.4232 x 10^7535
10,800	4.8498 x 10^7547	2.5289 x 10^7559	1.3360 x 10^7571	7.1510 x 10^7582	3.8778 x 10^7594	2.1305 x 10^7606	1.1858 x 10^7618	6.6873 x 10^7629	3.8205 x 10^7641	2.2113 x 10^7653
10,900	1.2966 x 10^7665	7.7028 x 10^7676	4.6357 x 10^7688	2.8263 x 10^7700	1.7457 x 10^7712	1.0923 x 10^7724	6.9244 x 10^7735	4.4467 x 10^7747	2.8927 x 10^7759	1.9064 x 10^7771
11,000	1.2727 x 10^7783	8.6075 x 10^7794	5.8970 x 10^7806	4.0926 x 10^7818	2.8772 x 10^7830	2.0491 x 10^7842	1.4782 x 10^7854	1.0803 x 10^7866	7.9971 x 10^7877	5.9967 x 10^7889
11,100	4.5549 x 10^7901	3.5047 x 10^7913	2.7314 x 10^7925	2.1564 x 10^7937	1.7244 x 10^7949	1.3968 x 10^7961	1.1460 x 10^7973	9.5244 x 10^7984	8.0176 x 10^7996	6.8363 x 10^8008
11,200	5.9041 x 10^8020	5.1648 x 10^8032	4.5762 x 10^8044	4.1069 x 10^8056	3.7332 x 10^8068	3.4371 x 10^8080	3.2052 x 10^8092	3.0273 x 10^8104	2.8960 x 10^8116	2.8060 x 10^8128
11,300	2.7536 x 10^8140	2.7369 x 10^8152	2.7551 x 10^8164	2.8090 x 10^8176	2.9005 x 10^8188	3.0335 x 10^8200	3.2130 x 10^8212	3.4467 x 10^8224	3.7447 x 10^8236	4.1203 x 10^8248
11,400	4.5915 x 10^8260	5.1819 x 10^8272	5.9228 x 10^8284	6.8559 x 10^8296	8.0370 x 10^8308	9.5417 x 10^8320	1.1472 x 10^8333	1.3968 x 10^8345	1.7224 x 10^8357	2.1510 x 10^8369
11,500	2.7202 x 10^8381	3.4837 x 10^8393	4.5182 x 10^8405	5.9342 x 10^8417	7.8928 x 10^8429	1.0630 x 10^8442	1.4500 x 10^8454	2.0028 x 10^8466	2.8013 x 10^8478	3.9678 x 10^8490
11,600	5.6910 x 10^8502	8.2659 x 10^8514	1.2157 x 10^8527	1.8106 x 10^8539	2.7307 x 10^8551	4.1702 x 10^8563	6.4488 x 10^8575	1.0098 x 10^8588	1.6012 x 10^8600	2.5708 x 10^8612
11,700	4.1796 x 10^8624	6.8807 x 10^8636	1.1469 x 10^8649	1.9359 x 10^8661	3.3086 x 10^8673	5.7258 x 10^8685	1.0033 x 10^8698	1.7800 x 10^8710	3.1978 x 10^8722	5.8169 x 10^8734
11,800	1.0713 x 10^8747	1.9978 x 10^8759	3.7723 x 10^8771	7.2118 x 10^8783	1.3959 x 10^8796	2.7359 x 10^8808	5.4291 x 10^8820	1.0907 x 10^8833	2.2189 x 10^8845	4.5700 x 10^8857
11,900	9.5297 x 10^8869	2.0119 x 10^8882	4.3007 x 10^8894	9.3076 x 10^8906	2.0394 x 10^8919	4.5242 x 10^8931	1.0161 x 10^8944	2.3105 x 10^8956	5.3193 x 10^8968	1.2397 x 10^8981
12,000	2.9255 x 10^8993	6.9889 x 10^9005	1.6903 x 10^9018	4.1389 x 10^9030	1.0260 x 10^9043	2.5749 x 10^9055	6.5421 x 10^9067	1.6827 x 10^9080	4.3818 x 10^9092	1.1551 x 10^9105
12,100	3.0827 x 10^9117	8.3288 x 10^9129	2.2780 x 10^9142	6.3075 x 10^9154	1.7680 x 10^9167	5.0170 x 10^9179	1.4411 x 10^9192	4.1909 x 10^9204	1.2337 x 10^9217	3.6766 x 10^9229
12,200	1.1091 x 10^9242	3.3872 x 10^9254	1.0471 x 10^9267	3.2770 x 10^9279	1.0381 x 10^9292	3.3290 x 10^9304	1.0806 x 10^9317	3.5511 x 10^9329	1.1812 x 10^9342	3.9773 x 10^9354
12,300	1.3556 x 10^9367	4.6771 x 10^9379	1.6334 x 10^9392	5.7745 x 10^9404	2.0663 x 10^9417	7.4848 x 10^9429	2.7443 x 10^9442	1.0185 x 10^9455	3.8261 x 10^9467	1.4549 x 10^9480
12,400	5.5999 x 10^9492	2.1816 x 10^9505	8.6034 x 10^9517	3.4340 x 10^9530	1.3874 x 10^9543	5.6737 x 10^9555	2.3484 x 10^9568	9.8392 x 10^9580	4.1724 x 10^9593	1.7908 x 10^9606
12,500	7.7802 x 10^9618	3.4210 x 10^9631	1.5225 x 10^9644	6.8586 x 10^9656	3.1270 x 10^9669	1.4430 x 10^9682	6.7399 x 10^9694	3.1861 x 10^9707	1.5244 x 10^9720	7.3821 x 10^9732
12,600	3.6181 x 10^9745	1.7947 x 10^9758	9.0108 x 10^9770	4.5786 x 10^9783	2.3547 x 10^9796	1.2256 x 10^9809	6.4562 x 10^9821	3.4421 x 10^9834	1.8573 x 10^9847	1.0142 x 10^9860
12,700	5.6057 x 10^9872	3.1355 x 10^9885	1.7750 x 10^9898	1.0169 x 10^9911	5.8964 x 10^9923	3.4600 x 10^9936	2.0548 x 10^9949	1.2349 x 10^9962	7.5115 x 10^9974	4.6237 x 10^9987
12,800	2.8804 x 10^10000	1.8159 x 10^10013	1.1585 x 10^10026	7.4806 x 10^10038	4.8880 x 10^10051	3.2323 x 10^10064	2.1630 x 10^10077	1.4648 x 10^10090	1.0039 x 10^10103	6.9625 x 10^10115
12,900	4.8867 x 10^10128	3.4708 x 10^10141	2.4946 x 10^10154	1.8144 x 10^10167	1.3355 x 10^10180	9.9479 x 10^10192	7.4982 x 10^10205	5.7193 x 10^10218	4.4145 x 10^10231	3.4481 x 10^10244
13,000	2.7254 x 10^10257	2.1798 x 10^10270	1.7643 x 10^10283	1.4449 x 10^10296	1.1975 x 10^10309	1.0043 x 10^10322	8.5232 x 10^10334	7.3192 x 10^10347	6.3600 x 10^10360	5.5923 x 10^10373
13,100	4.9758 x 10^10386	4.4798 x 10^10399	4.0812 x 10^10412	3.7622 x 10^10425	3.5094 x 10^10438	3.3124 x 10^10451	3.1636 x 10^10464	3.0573 x 10^10477	2.9896 x 10^10490	2.9580 x 10^10503
13,200	2.9615 x 10^10516	3.0001 x 10^10529	3.0752 x 10^10542	3.1895 x 10^10555	3.3472 x 10^10568	3.5543 x 10^10581	3.8188 x 10^10594	4.1515 x 10^10607	4.5665 x 10^10620	5.0823 x 10^10633
13,300	5.7233 x 10^10646	6.5211 x 10^10659	7.5179 x 10^10672	8.7694 x 10^10685	1.0349 x 10^10699	1.2358 x 10^10712	1.4932 x 10^10725	1.8253 x 10^10738	2.2577 x 10^10751	2.8253 x 10^10764
13,400	3.5772 x 10^10777	4.5826 x 10^10790	5.9395 x 10^10803	7.7889 x 10^10816	1.0334 x 10^10830	1.3872 x 10^10843	1.8840 x 10^10856	2.5888 x 10^10869	3.5990 x 10^10882	5.0622 x 10^10895
13,500	7.2038 x 10^10908	1.0371 x 10^10922	1.5107 x 10^10935	2.2264 x 10^10948	3.3195 x 10^10961	5.0072 x 10^10974	7.6416 x 10^10987	1.1798 x 10^11001	1.8429 x 10^11014	2.9125 x 10^11027
13,600	4.6565 x 10^11040	7.5320 x 10^11053	1.2325 x 10^11067	2.0405 x 10^11080	3.4177 x 10^11093	5.7911 x 10^11106	9.9273 x 10^11119	1.7216 x 10^11133	3.0205 x 10^11146	5.3613 x 10^11159
13,700	9.6270 x 10^11172	1.7488 x 10^11186	3.2138 x 10^11199	5.9751 x 10^11212	1.1238 x 10^11226	2.1382 x 10^11239	4.1159 x 10^11252	8.0147 x 10^11265	1.5788 x 10^11279	3.1463 x 10^11292
13,800	6.3430 x 10^11305	1.2936 x 10^11319	2.6689 x 10^11332	5.5702 x 10^11345	1.1760 x 10^11359	2.5119 x 10^11372	5.4273 x 10^11385	1.1862 x 10^11399	2.6228 x 10^11412	5.8665 x 10^11425
13,900	1.3273 x 10^11439	3.0381 x 10^11452	7.0345 x 10^11465	1.6476 x 10^11479	3.9037 x 10^11492	9.3561 x 10^11505	2.2683 x 10^11519	5.5632 x 10^11532	1.3801 x 10^11546	3.4636 x 10^11559
14,000	8.7928 x 10^11572	2.2579 x 10^11586	5.8652 x 10^11599	1.5411 x 10^11613	4.0962 x 10^11626	1.1013 x 10^11640	2.9952 x 10^11653	8.2399 x 10^11666	2.2929 x 10^11680	6.4543 x 10^11693
14,100	1.8377 x 10^11707	5.2929 x 10^11720	1.5419 x 10^11734	4.5439 x 10^11747	1.3544 x 10^11761	4.0838 x 10^11774	1.2454 x 10^11788	3.8421 x 10^11801	1.1988 x 10^11815	3.7840 x 10^11828
14,200	1.2080 x 10^11842	3.9010 x 10^11855	1.2742 x 10^11869	4.2098 x 10^11882	1.4068 x 10^11896	4.7554 x 10^11909	1.6258 x 10^11923	5.6225 x 10^11936	1.9666 x 10^11950	6.9581 x 10^11963
14,300	2.4900 x 10^11977	9.0127 x 10^11990	3.2996 x 10^12004	1.2218 x 10^12018	4.5763 x 10^12031	1.7336 x 10^12045	6.6428 x 10^12058	2.5744 x 10^12072	1.0091 x 10^12086	4.0010 x 10^12099
14,400	1.6044 x 10^12113	6.5074 x 10^12126	2.6695 x 10^12140	1.1076 x 10^12154	4.6482 x 10^12167	1.9729 x 10^12181	8.4697 x 10^12194	3.6775 x 10^12208	1.6150 x 10^12222	7.1733 x 10^12235
14,500	3.2224 x 10^12249	1.4641 x 10^12263	6.7282 x 10^12276	3.1271 x 10^12290	1.4699 x 10^12304	6.9886 x 10^12317	3.3604 x 10^12331	1.6342 x 10^12345	8.0381 x 10^12358	3.9986 x 10^12372
14,600	2.0117 x 10^12386	1.0236 x 10^12400	5.2681 x 10^12413	2.7419 x 10^12427	1.4433 x 10^12441	7.6841 x 10^12454	4.1374 x 10^12468	2.2530 x 10^12482	1.2408 x 10^12496	6.9112 x 10^12509
14,700	3.8931 x 10^12523	2.2179 x 10^12537	1.2779 x 10^12551	7.4465 x 10^12564	4.3883 x 10^12578	2.6154 x 10^12592	1.5764 x 10^12606	9.6101 x 10^12619	5.9246 x 10^12633	3.6939 x 10^12647
14,800	2.3291 x 10^12661	1.4852 x 10^12675	9.5786 x 10^12688	6.2472 x 10^12702	4.1206 x 10^12716	2.7486 x 10^12730	1.8542 x 10^12744	1.2649 x 10^12758	8.7276 x 10^12771	6.0896 x 10^12785
14,900	4.2969 x 10^12799	3.0662 x 10^12813	2.2128 x 10^12827	1.6149 x 10^12841	1.1918 x 10^12855	8.8960 x 10^12868	6.7148 x 10^12882	5.1255 x 10^12896	3.9565 x 10^12910	3.0886 x 10^12924
15,000	2.4383 x 10^12938	1.9466 x 10^12952	1.5716 x 10^12966	1.2831 x 10^12980	1.0594 x 10^12994	8.8455 x 10^13007	7.4687 x 10^13021	6.3772 x 10^13035	5.5065 x 10^13049	4.8082 x 10^13063
15,100	4.2457 x 10^13077	3.7912 x 10^13091	3.4234 x 10^13105	3.1261 x 10^13119	2.8867 x 10^13133	2.6956 x 10^13147	2.5454 x 10^13161	2.4306 x 10^13175	2.3471 x 10^13189	2.2919 x 10^13203
15,200	2.2631 x 10^13217	2.2598 x 10^13231	2.2819 x 10^13245	2.3300 x 10^13259	2.4058 x 10^13273	2.5119 x 10^13287	2.6522 x 10^13301	2.8317 x 10^13315	3.0572 x 10^13329	3.3377 x 10^13343
15,300	3.6848 x 10^13357	4.1135 x 10^13371	4.6436 x 10^13385	5.3008 x 10^13399	6.1187 x 10^13413	7.1418 x 10^13427	8.4295 x 10^13441	1.0060 x 10^13456	1.2141 x 10^13470	1.4817 x 10^13484
15,400	1.8284 x 10^13498	2.2815 x 10^13512	2.8788 x 10^13526	3.6730 x 10^13540	4.7387 x 10^13554	6.1819 x 10^13568	8.1548 x 10^13582	1.0877 x 10^13597	1.4671 x 10^13611	2.0009 x 10^13625
15,500	2.7594 x 10^13639	3.8479 x 10^13653	5.4256 x 10^13667	7.7357 x 10^13681	1.1152 x 10^13696	1.6257 x 10^13710	2.3964 x 10^13724	3.5717 x 10^13738	5.3828 x 10^13752	8.2028 x 10^13766
15,600	1.2639 x 10^13781	1.9692 x 10^13795	3.1023 x 10^13809	4.9419 x 10^13823	7.9599 x 10^13837	1.2963 x 10^13852	2.1348 x 10^13866	3.5546 x 10^13880	5.9847 x 10^13894	1.0188 x 10^13909
15,700	1.7537 x 10^13923	3.0522 x 10^13937	5.3714 x 10^13951	9.5579 x 10^13965	1.7196 x 10^13980	3.1283 x 10^13994	5.7543 x 10^14008	1.0702 x 10^14023	2.0125 x 10^14037	3.8266 x 10^14051
15,800	7.3569 x 10^14065	1.4301 x 10^14080	2.8108 x 10^14094	5.5859 x 10^14108	1.1224 x 10^14123	2.2803 x 10^14137	4.6843 x 10^14151	9.7294 x 10^14165	2.0432 x 10^14180	4.3384 x 10^14194
15,900	9.3142 x 10^14208	2.0218 x 10^14223	4.4374 x 10^14237	9.8472 x 10^14251	2.2094 x 10^14266	5.0122 x 10^14280	1.1496 x 10^14295	2.6661 x 10^14309	6.2516 x 10^14323	1.4821 x 10^14338
16,000	3.5526 x 10^14352	8.6101 x 10^14366	2.1098 x 10^14381	5.2271 x 10^14395	1.3093 x 10^14410	3.3162 x 10^14424	8.4917 x 10^14438	2.1985 x 10^14453	5.7549 x 10^14467	1.5231 x 10^14482
16,100	4.0756 x 10^14496	1.1026 x 10^14511	3.0161 x 10^14525	8.3413 x 10^14539	2.3323 x 10^14554	6.5937 x 10^14568	1.8846 x 10^14583	5.4464 x 10^14597	1.5913 x 10^14612	4.7008 x 10^14626
16,200	1.4040 x 10^14641	4.2395 x 10^14655	1.2943 x 10^14670	3.9951 x 10^14684	1.2467 x 10^14699	3.9338 x 10^14713	1.2548 x 10^14728	4.0472 x 10^14742	1.3197 x 10^14757	4.3507 x 10^14771
16,300	1.4501 x 10^14786	4.8866 x 10^14800	1.6648 x 10^14815	5.7347 x 10^14829	1.9971 x 10^14844	7.0315 x 10^14858	2.5030 x 10^14873	9.0080 x 10^14887	3.2775 x 10^14902	1.2056 x 10^14917
16,400	4.4841 x 10^14931	1.6860 x 10^14946	6.4095 x 10^14960	2.4633 x 10^14975	9.5718 x 10^14989	3.7602 x 10^15004	1.4934 x 10^15019	5.9965 x 10^15033	2.4343 x 10^15048	9.9907 x 10^15062
16,500	4.1454 x 10^15077	1.7390 x 10^15092	7.3752 x 10^15106	3.1623 x 10^15121	1.3708 x 10^15136	6.0076 x 10^15150	2.6617 x 10^15165	1.1923 x 10^15180	5.3995 x 10^15194	2.4721 x 10^15209
16,600	1.1442 x 10^15224	5.3545 x 10^15238	2.5331 x 10^15253	1.2115 x 10^15268	5.8585 x 10^15282	2.8639 x 10^15297	1.4154 x 10^15312	7.0720 x 10^15326	3.5722 x 10^15341	1.8242 x 10^15356
16,700	9.4182 x 10^15370	4.9157 x 10^15385	2.5939 x 10^15400	1.3837 x 10^15415	7.4626 x 10^15429	4.0688 x 10^15444	2.2427 x 10^15459	1.2497 x 10^15474	7.0407 x 10^15488	4.0099 x 10^15503
16,800	2.3088 x 10^15518	1.3439 x 10^15533	7.9090 x 10^15547	4.7052 x 10^15562	2.8299 x 10^15577	1.7207 x 10^15592	1.0577 x 10^15607	6.5729 x 10^15621	4.1294 x 10^15636	2.6226 x 10^15651
16,900	1.6839 x 10^15666	1.0930 x 10^15681	7.1728 x 10^15695	4.7585 x 10^15710	3.1913 x 10^15725	2.1637 x 10^15740	1.4831 x 10^15755	1.0276 x 10^15770	7.1991 x 10^15784	5.0982 x 10^15799
17,000	3.6499 x 10^15814	2.6417 x 10^15829	1.9329 x 10^15844	1.4297 x 10^15859	1.0691 x 10^15874	8.0821 x 10^15888	6.1765 x 10^15903	4.7718 x 10^15918	3.7269 x 10^15933	2.9427 x 10^15948
17,100	2.3488 x 10^15963	1.8953 x 10^15978	1.5461 x 10^15993	1.2750 x 10^16008	1.0629 x 10^16023	8.9586 x 10^16037	7.6327 x 10^16052	6.5741 x 10^16067	5.7242 x 10^16082	5.0386 x 10^16097
17,200	4.4836 x 10^16112	4.0333 x 10^16127	3.6678 x 10^16142	3.3719 x 10^16157	3.1337 x 10^16172	2.9442 x 10^16187	2.7963 x 10^16202	2.6848 x 10^16217	2.6059 x 10^16232	2.5570 x 10^16247
17,300	2.5364 x 10^16262	2.5434 x 10^16277	2.5782 x 10^16292	2.6421 x 10^16307	2.7371 x 10^16322	2.8664 x 10^16337	3.0346 x 10^16352	3.2478 x 10^16367	3.5138 x 10^16382	3.8431 x 10^16397
17,400	4.2491 x 10^16412	4.7492 x 10^16427	5.3661 x 10^16442	6.1293 x 10^16457	7.0773 x 10^16472	8.2611 x 10^16487	9.7481 x 10^16502	1.1628 x 10^16518	1.4022 x 10^16533	1.7093 x 10^16548
17,500	2.1063 x 10^16563	2.6239 x 10^16578	3.3044 x 10^16593	4.2066 x 10^16608	5.4136 x 10^16623	7.0428 x 10^16638	9.2622 x 10^16653	1.2313 x 10^16669	1.6548 x 10^16684	2.2483 x 10^16699
17,600	3.0877 x 10^16714	4.2869 x 10^16729	6.0166 x 10^16744	8.5361 x 10^16759	1.2242 x 10^16775	1.7750 x 10^16790	2.6015 x 10^16805	3.8543 x 10^16820	5.7728 x 10^16835	8.7403 x 10^16850
17,700	1.3377 x 10^16866	2.0697 x 10^16881	3.2371 x 10^16896	5.1182 x 10^16911	8.1804 x 10^16926	1.3217 x 10^16942	2.1587 x 10^16957	3.5642 x 10^16972	5.9488 x 10^16987	1.0036 x 10^17003
17,800	1.7118 x 10^17018	2.9514 x 10^17033	5.1441 x 10^17048	9.0634 x 10^17063	1.6142 x 10^17079	2.9063 x 10^17094	5.2896 x 10^17109	9.7319 x 10^17124	1.8100 x 10^17140	3.4029 x 10^17155
17,900	6.4675 x 10^17170	1.2425 x 10^17186	2.4132 x 10^17201	4.7377 x 10^17216	9.4027 x 10^17231	1.8863 x 10^17247	3.8256 x 10^17262	7.8430 x 10^17277	1.6253 x 10^17293	3.4050 x 10^17308
18,000	7.2110 x 10^17323	1.5437 x 10^17339	3.3407 x 10^17354	7.3080 x 10^17369	1.6160 x 10^17385	3.6126 x 10^17400	8.1637 x 10^17415	1.8648 x 10^17431	4.3062 x 10^17446	1.0051 x 10^17462
18,100	2.3719 x 10^17477	5.6578 x 10^17492	1.3642 x 10^17508	3.3253 x 10^17523	8.1934 x 10^17538	2.0408 x 10^17554	5.1384 x 10^17569	1.3078 x 10^17585	3.3649 x 10^17600	8.7519 x 10^17615
18,200	2.3010 x 10^17631	6.1154 x 10^17646	1.6430 x 10^17662	4.4621 x 10^17677	1.2250 x 10^17693	3.3997 x 10^17708	9.5374 x 10^17723	2.7047 x 10^17739	7.7536 x 10^17754	2.2468 x 10^17770
18,300	6.5820 x 10^17785	1.9490 x 10^17801	5.8343 x 10^17816	1.7654 x 10^17832	5.4002 x 10^17847	1.6697 x 10^17863	5.2192 x 10^17878	1.6491 x 10^17894	5.2673 x 10^17909	1.7006 x 10^17925
18,400	5.5507 x 10^17940	1.8313 x 10^17956	6.1078 x 10^17971	2.0592 x 10^17987	7.0179 x 10^18002	2.4177 x 10^18018	8.4199 x 10^18033	2.9641 x 10^18049	1.0548 x 10^18065	3.7946 x 10^18080
18,500	1.3799 x 10^18096	5.0725 x 10^18111	1.8849 x 10^18127	7.0803 x 10^18142	2.6884 x 10^18158	1.0319 x 10^18174	4.0041 x 10^18189	1.5705 x 10^18205	6.2271 x 10^18220	2.4958 x 10^18236
18,600	1.0112 x 10^18252	4.1416 x 10^18267	1.7147 x 10^18283	7.1763 x 10^18298	3.0360 x 10^18314	1.2984 x 10^18330	5.6132 x 10^18345	2.4530 x 10^18361	1.0836 x 10^18377	4.8392 x 10^18392
18,700	2.1845 x 10^18408	9.9685 x 10^18423	4.5983 x 10^18439	2.1442 x 10^18455	1.0107 x 10^18471	4.8160 x 10^18486	2.3197 x 10^18502	1.1295 x 10^18518	5.5595 x 10^18533	2.7661 x 10^18549
18,800	1.3912 x 10^18565	7.0738 x 10^18580	3.6356 x 10^18596	1.8889 x 10^18612	9.9204 x 10^18627	5.2668 x 10^18643	2.8266 x 10^18659	1.5334 x 10^18675	8.4099 x 10^18690	4.6622 x 10^18706
18,900	2.6127 x 10^18722	1.4801 x 10^18738	8.4761 x 10^18753	4.9067 x 10^18769	2.8713 x 10^18785	1.6985 x 10^18801	1.0157 x 10^18817	6.1398 x 10^18832	3.7517 x 10^18848	2.3175 x 10^18864
19,000	1.4471 x 10^18880	9.1343 x 10^18895	5.8285 x 10^18911	3.7595 x 10^18927	2.4513 x 10^18943	1.6157 x 10^18959	1.0766 x 10^18975	7.2514 x 10^18990	4.9373 x 10^19006	3.3983 x 10^19022
19,100	2.3645 x 10^19038	1.6630 x 10^19054	1.1824 x 10^19070	8.4987 x 10^19085	6.1748 x 10^19101	4.5351 x 10^19117	3.3671 x 10^19133	2.5272 x 10^19149	1.9174 x 10^19165	1.4705 x 10^19181
19,200	1.1401 x 10^19197	8.9361 x 10^19212	7.0799 x 10^19228	5.6704 x 10^19244	4.5909 x 10^19260	3.7574 x 10^19276	3.1086 x 10^19292	2.5999 x 10^19308	2.1982 x 10^19324	1.8787 x 10^19340
19,300	1.6231 x 10^19356	1.4176 x 10^19372	1.2516 x 10^19388	1.1171 x 10^19404	1.0079 x 10^19420	9.1928 x 10^19435	8.4757 x 10^19451	7.8997 x 10^19467	7.4430 x 10^19483	7.0892 x 10^19499
19,400	6.8257 x 10^19515	6.6436 x 10^19531	6.5368 x 10^19547	6.5019 x 10^19563	6.5375 x 10^19579	6.6451 x 10^19595	6.8279 x 10^19611	7.0923 x 10^19627	7.4473 x 10^19643	7.9052 x 10^19659
19,500	8.4827 x 10^19675	9.2017 x 10^19691	1.0090 x 10^19708	1.1185 x 10^19724	1.2534 x 10^19740	1.4200 x 10^19756	1.6261 x 10^19772	1.8826 x 10^19788	2.2032 x 10^19804	2.6066 x 10^19820
19,600	3.1174 x 10^19836	3.7690 x 10^19852	4.6066 x 10^19868	5.6916 x 10^19884	7.1090 x 10^19900	8.9763 x 10^19916	1.1457 x 10^19933	1.4784 x 10^19949	1.9285 x 10^19965	2.5431 x 10^19981
19,700	3.3901 x 10^19997	4.5686 x 10^20013	6.2240 x 10^20029	8.5718 x 10^20045	1.1934 x 10^20062	1.6796 x 10^20078	2.3898 x 10^20094	3.4374 x 10^20110	4.9982 x 10^20126	7.3470 x 10^20142
19,800	1.0917 x 10^20159	1.6400 x 10^20175	2.4906 x 10^20191	3.8237 x 10^20207	5.9344 x 10^20223	9.3109 x 10^20239	1.4768 x 10^20256	2.3679 x 10^20272	3.8384 x 10^20288	6.2899 x 10^20304
19,900	1.0419 x 10^20321	1.7450 x 10^20337	2.9543 x 10^20353	5.0564 x 10^20369	8.7488 x 10^20385	1.5303 x 10^20402	2.7060 x 10^20418	4.8373 x 10^20434	8.7420 x 10^20450	1.5971 x 10^20467

ThatDonGuy

Threads: 122
Posts: 6677

Joined: Jun 22, 2011

January 28th, 2020 at 4:39:27 PM permalink

	0	10	20	30	40	50	60	70	80	90
20,000	2.9498 x 10^20483	5.5077 x 10^20499	1.0396 x 10^20516	1.9838 x 10^20532	3.8271 x 10^20548	7.4638 x 10^20564	1.4715 x 10^20581	2.9330 x 10^20597	5.9101 x 10^20613	1.2039 x 10^20630
20,100	2.4793 x 10^20646	5.1617 x 10^20662	1.0864 x 10^20679	2.3116 x 10^20695	4.9724 x 10^20711	1.0813 x 10^20728	2.3772 x 10^20744	5.2836 x 10^20760	1.1872 x 10^20777	2.6967 x 10^20793
20,200	6.1930 x 10^20809	1.4377 x 10^20826	3.3746 x 10^20842	8.0073 x 10^20858	1.9208 x 10^20875	4.6582 x 10^20891	1.1420 x 10^20908	2.8307 x 10^20924	7.0934 x 10^20940	1.7969 x 10^20957
20,300	4.6022 x 10^20973	1.1916 x 10^20990	3.1192 x 10^21006	8.2546 x 10^21022	2.2084 x 10^21039	5.9733 x 10^21055	1.6334 x 10^21072	4.5155 x 10^21088	1.2620 x 10^21105	3.5659 x 10^21121
20,400	1.0186 x 10^21138	2.9418 x 10^21154	8.5893 x 10^21170	2.5353 x 10^21187	7.5661 x 10^21203	2.2827 x 10^21220	6.9627 x 10^21236	2.1471 x 10^21253	6.6939 x 10^21269	2.1098 x 10^21286
20,500	6.7232 x 10^21302	2.1659 x 10^21319	7.0546 x 10^21335	2.3230 x 10^21352	7.7336 x 10^21368	2.6029 x 10^21385	8.8572 x 10^21401	3.0471 x 10^21418	1.0598 x 10^21435	3.7267 x 10^21451
20,600	1.3248 x 10^21468	4.7620 x 10^21484	1.7304 x 10^21501	6.3574 x 10^21517	2.3613 x 10^21534	8.8676 x 10^21550	3.3667 x 10^21567	1.2923 x 10^21584	5.0151 x 10^21600	1.9677 x 10^21617
20,700	7.8056 x 10^21633	3.1305 x 10^21650	1.2693 x 10^21667	5.2037 x 10^21683	2.1568 x 10^21700	9.0380 x 10^21716	3.8291 x 10^21733	1.6401 x 10^21750	7.1031 x 10^21766	3.1101 x 10^21783
20,800	1.3768 x 10^21800	6.1621 x 10^21816	2.7884 x 10^21833	1.2757 x 10^21850	5.9012 x 10^21866	2.7598 x 10^21883	1.3049 x 10^21900	6.2386 x 10^21916	3.0154 x 10^21933	1.4736 x 10^21950
20,900	7.2811 x 10^21966	3.6373 x 10^21983	1.8371 x 10^22000	9.3817 x 10^22016	4.8439 x 10^22033	2.5286 x 10^22050	1.3346 x 10^22067	7.1223 x 10^22083	3.8428 x 10^22100	2.0963 x 10^22117
21,000	1.1562 x 10^22134	6.4481 x 10^22150	3.6357 x 10^22167	2.0727 x 10^22184	1.1947 x 10^22201	6.9627 x 10^22217	4.1028 x 10^22234	2.4443 x 10^22251	1.4724 x 10^22268	8.9681 x 10^22284
21,100	5.5227 x 10^22301	3.4386 x 10^22318	2.1648 x 10^22335	1.3779 x 10^22352	8.8686 x 10^22368	5.7711 x 10^22385	3.7971 x 10^22402	2.5261 x 10^22419	1.6991 x 10^22436	1.1556 x 10^22453
21,200	7.9469 x 10^22469	5.5255 x 10^22486	3.8846 x 10^22503	2.7613 x 10^22520	1.9847 x 10^22537	1.4423 x 10^22554	1.0598 x 10^22571	7.8744 x 10^22587	5.9155 x 10^22604	4.4934 x 10^22621
21,300	3.4511 x 10^22638	2.6801 x 10^22655	2.1045 x 10^22672	1.6709 x 10^22689	1.3414 x 10^22706	1.0888 x 10^22723	8.9374 x 10^22739	7.4174 x 10^22756	6.2244 x 10^22773	5.2815 x 10^22790
21,400	4.5314 x 10^22807	3.9311 x 10^22824	3.4484 x 10^22841	3.0586 x 10^22858	2.7432 x 10^22875	2.4877 x 10^22892	2.2812 x 10^22909	2.1152 x 10^22926	1.9831 x 10^22943	1.8801 x 10^22960
21,500	1.8022 x 10^22977	1.7469 x 10^22994	1.7122 x 10^23011	1.6970 x 10^23028	1.7006 x 10^23045	1.7233 x 10^23062	1.7659 x 10^23079	1.8297 x 10^23096	1.9170 x 10^23113	2.0309 x 10^23130
21,600	2.1756 x 10^23147	2.3568 x 10^23164	2.5815 x 10^23181	2.8594 x 10^23198	3.2026 x 10^23215	3.6271 x 10^23232	4.1539 x 10^23249	4.8105 x 10^23266	5.6333 x 10^23283	6.6707 x 10^23300
21,700	7.9877 x 10^23317	9.6718 x 10^23334	1.1842 x 10^23352	1.4662 x 10^23369	1.8357 x 10^23386	2.3241 x 10^23403	2.9755 x 10^23420	3.8522 x 10^23437	5.0431 x 10^23454	6.6763 x 10^23471
21,800	8.9377 x 10^23488	1.2099 x 10^23506	1.6563 x 10^23523	2.2929 x 10^23540	3.2097 x 10^23557	4.5437 x 10^23574	6.5044 x 10^23591	9.4159 x 10^23608	1.3783 x 10^23626	2.0405 x 10^23643
21,900	3.0546 x 10^23660	4.6242 x 10^23677	7.0791 x 10^23694	1.0959 x 10^23712	1.7157 x 10^23729	2.7163 x 10^23746	4.3488 x 10^23763	7.0409 x 10^23780	1.1527 x 10^23798	1.9087 x 10^23815
22,000	3.1959 x 10^23832	5.4116 x 10^23849	9.2667 x 10^23866	1.6047 x 10^23884	2.8102 x 10^23901	4.9768 x 10^23918	8.9134 x 10^23935	1.6143 x 10^23953	2.9569 x 10^23970	5.4773 x 10^23987
22,100	1.0260 x 10^24005	1.9437 x 10^24022	3.7239 x 10^24039	7.2151 x 10^24056	1.4137 x 10^24074	2.8013 x 10^24091	5.6139 x 10^24108	1.1377 x 10^24126	2.3319 x 10^24143	4.8335 x 10^24160
22,200	1.0132 x 10^24178	2.1480 x 10^24195	4.6054 x 10^24212	9.9858 x 10^24229	2.1897 x 10^24247	4.8563 x 10^24264	1.0892 x 10^24282	2.4706 x 10^24299	5.6677 x 10^24316	1.3149 x 10^24334
22,300	3.0853 x 10^24351	7.3216 x 10^24368	1.7571 x 10^24386	4.2650 x 10^24403	1.0469 x 10^24421	2.5992 x 10^24438	6.5265 x 10^24455	1.6573 x 10^24473	4.2565 x 10^24490	1.1056 x 10^24508
22,400	2.9046 x 10^24525	7.7173 x 10^24542	2.0737 x 10^24560	5.6360 x 10^24577	1.5491 x 10^24595	4.3067 x 10^24612	1.2109 x 10^24630	3.4435 x 10^24647	9.9040 x 10^24664	2.8809 x 10^24682
22,500	8.4760 x 10^24699	2.5221 x 10^24717	7.5907 x 10^24734	2.3105 x 10^24752	7.1134 x 10^24769	2.2149 x 10^24787	6.9758 x 10^24804	2.2220 x 10^24822	7.1588 x 10^24839	2.3327 x 10^24857
22,600	7.6882 x 10^24874	2.5628 x 10^24892	8.6409 x 10^24909	2.9467 x 10^24927	1.0163 x 10^24945	3.5458 x 10^24962	1.2511 x 10^24980	4.4655 x 10^24997	1.6120 x 10^25015	5.8859 x 10^25032
22,700	2.1737 x 10^25050	8.1198 x 10^25067	3.0679 x 10^25085	1.1724 x 10^25103	4.5319 x 10^25120	1.7719 x 10^25138	7.0073 x 10^25155	2.8030 x 10^25173	1.1341 x 10^25191	4.6413 x 10^25208
22,800	1.9212 x 10^25226	8.0446 x 10^25243	3.4071 x 10^25261	1.4595 x 10^25279	6.3247 x 10^25296	2.7721 x 10^25314	1.2290 x 10^25332	5.5117 x 10^25349	2.5002 x 10^25367	1.1472 x 10^25385
22,900	5.3246 x 10^25402	2.4998 x 10^25420	1.1871 x 10^25438	5.7027 x 10^25455	2.7710 x 10^25473	1.3619 x 10^25491	6.7716 x 10^25508	3.4056 x 10^25526	1.7325 x 10^25544	8.9159 x 10^25561
23,000	4.6412 x 10^25579	2.4439 x 10^25597	1.3017 x 10^25615	7.0143 x 10^25632	3.8231 x 10^25650	2.1079 x 10^25668	1.1756 x 10^25686	6.6330 x 10^25703	3.7856 x 10^25721	2.1856 x 10^25739
23,100	1.2764 x 10^25757	7.5412 x 10^25774	4.5069 x 10^25792	2.7247 x 10^25810	1.6664 x 10^25828	1.0310 x 10^25846	6.4526 x 10^25863	4.0853 x 10^25881	2.6166 x 10^25899	1.6953 x 10^25917
23,200	1.1112 x 10^25935	7.3682 x 10^25952	4.9425 x 10^25970	3.3538 x 10^25988	2.3023 x 10^26006	1.5989 x 10^26024	1.1233 x 10^26042	7.9837 x 10^26059	5.7403 x 10^26077	4.1754 x 10^26095
23,300	3.0725 x 10^26113	2.2873 x 10^26131	1.7226 x 10^26149	1.3124 x 10^26167	1.0116 x 10^26185	7.8889 x 10^26202	6.2236 x 10^26220	4.9671 x 10^26238	4.0106 x 10^26256	3.2762 x 10^26274
23,400	2.7075 x 10^26292	2.2637 x 10^26310	1.9148 x 10^26328	1.6386 x 10^26346	1.4187 x 10^26364	1.2426 x 10^26382	1.1012 x 10^26400	9.8733 x 10^26417	8.9557 x 10^26435	8.2187 x 10^26453
23,500	7.6308 x 10^26471	7.1680 x 10^26489	6.8123 x 10^26507	6.5503 x 10^26525	6.3723 x 10^26543	6.2719 x 10^26561	6.2457 x 10^26579	6.2926 x 10^26597	6.4145 x 10^26615	6.6156 x 10^26633
23,600	6.9033 x 10^26651	7.2882 x 10^26669	7.7853 x 10^26687	8.4141 x 10^26705	9.2009 x 10^26723	1.0179 x 10^26742	1.1395 x 10^26760	1.2907 x 10^26778	1.4791 x 10^26796	1.7150 x 10^26814
23,700	2.0121 x 10^26832	2.3885 x 10^26850	2.8687 x 10^26868	3.4863 x 10^26886	4.2868 x 10^26904	5.3335 x 10^26922	6.7142 x 10^26940	8.5524 x 10^26958	1.1022 x 10^26977	1.4374 x 10^26995
23,800	1.8968 x 10^27013	2.5326 x 10^27031	3.4215 x 10^27049	4.6773 x 10^27067	6.4698 x 10^27085	9.0553 x 10^27103	1.2824 x 10^27122	1.8378 x 10^27140	2.6650 x 10^27158	3.9104 x 10^27176
23,900	5.8059 x 10^27194	8.7227 x 10^27212	1.3260 x 10^27231	2.0399 x 10^27249	3.1755 x 10^27267	5.0019 x 10^27285	7.9728 x 10^27303	1.2859 x 10^27322	2.0988 x 10^27340	3.4664 x 10^27358
24,000	5.7934 x 10^27376	9.7981 x 10^27394	1.6768 x 10^27413	2.9040 x 10^27431	5.0894 x 10^27449	9.0259 x 10^27467	1.6198 x 10^27486	2.9418 x 10^27504	5.4065 x 10^27522	1.0055 x 10^27541
24,100	1.8924 x 10^27559	3.6043 x 10^27577	6.9471 x 10^27595	1.3550 x 10^27614	2.6746 x 10^27632	5.3428 x 10^27650	1.0800 x 10^27669	2.2095 x 10^27687	4.5744 x 10^27705	9.5842 x 10^27723
24,200	2.0321 x 10^27742	4.3607 x 10^27760	9.4697 x 10^27778	2.0811 x 10^27797	4.6289 x 10^27815	1.0419 x 10^27834	2.3735 x 10^27852	5.4721 x 10^27870	1.2767 x 10^27889	3.0149 x 10^27907
24,300	7.2051 x 10^27925	1.7426 x 10^27944	4.2657 x 10^27962	1.0567 x 10^27981	2.6496 x 10^27999	6.7237 x 10^28017	1.7268 x 10^28036	4.4884 x 10^28054	1.1807 x 10^28073	3.1439 x 10^28091
24,400	8.4721 x 10^28109	2.3106 x 10^28128	6.3784 x 10^28146	1.7820 x 10^28165	5.0392 x 10^28183	1.4422 x 10^28202	4.1778 x 10^28220	1.2248 x 10^28239	3.6348 x 10^28257	1.0917 x 10^28276
24,500	3.3189 x 10^28294	1.0212 x 10^28313	3.1805 x 10^28331	1.0025 x 10^28350	3.1988 x 10^28368	1.0330 x 10^28387	3.3769 x 10^28405	1.1172 x 10^28424	3.7417 x 10^28442	1.2683 x 10^28461
24,600	4.3520 x 10^28479	1.5114 x 10^28498	5.3134 x 10^28516	1.8907 x 10^28535	6.8099 x 10^28553	2.4828 x 10^28572	9.1626 x 10^28590	3.4227 x 10^28609	1.2942 x 10^28628	4.9538 x 10^28646
24,700	1.9193 x 10^28665	7.5274 x 10^28683	2.9884 x 10^28702	1.2009 x 10^28721	4.8854 x 10^28739	2.0117 x 10^28758	8.3860 x 10^28776	3.5386 x 10^28795	1.5115 x 10^28814	6.5359 x 10^28832
24,800	2.8609 x 10^28851	1.2676 x 10^28870	5.6864 x 10^28888	2.5821 x 10^28907	1.1869 x 10^28926	5.5233 x 10^28944	2.6019 x 10^28963	1.2408 x 10^28982	5.9905 x 10^29000	2.9278 x 10^29019
24,900	1.4486 x 10^29038	7.2558 x 10^29056	3.6792 x 10^29075	1.8887 x 10^29094	9.8158 x 10^29112	5.1644 x 10^29131	2.7508 x 10^29150	1.4833 x 10^29169	8.0981 x 10^29187	4.4758 x 10^29206
25,000	2.5044 x 10^29225	1.4187 x 10^29244	8.1370 x 10^29262	4.7247 x 10^29281	2.7775 x 10^29300	1.6531 x 10^29319	9.9613 x 10^29337	6.0771 x 10^29356	3.7536 x 10^29375	2.3473 x 10^29394
25,100	1.4862 x 10^29413	9.5275 x 10^29431	6.1837 x 10^29450	4.0635 x 10^29469	2.7035 x 10^29488	1.8212 x 10^29507	1.2422 x 10^29526	8.5784 x 10^29544	5.9981 x 10^29563	4.2464 x 10^29582
25,200	3.0439 x 10^29601	2.2092 x 10^29620	1.6235 x 10^29639	1.2081 x 10^29658	9.1021 x 10^29676	6.9438 x 10^29695	5.3637 x 10^29714	4.1952 x 10^29733	3.3224 x 10^29752	2.6643 x 10^29771
25,300	2.1634 x 10^29790	1.7788 x 10^29809	1.4810 x 10^29828	1.2485 x 10^29847	1.0658 x 10^29866	9.2133 x 10^29884	8.0646 x 10^29903	7.1481 x 10^29922	6.4157 x 10^29941	5.8311 x 10^29960
25,400	5.3666 x 10^29979	5.0016 x 10^29998	4.7203 x 10^30017	4.5112 x 10^30036	4.3660 x 10^30055	4.2788 x 10^30074	4.2466 x 10^30093	4.2680 x 10^30112	4.3439 x 10^30131	4.4772 x 10^30150
25,500	4.6732 x 10^30169	4.9397 x 10^30188	5.2877 x 10^30207	5.7321 x 10^30226	6.2930 x 10^30245	6.9966 x 10^30264	7.8778 x 10^30283	8.9830 x 10^30302	1.0373 x 10^30322	1.2132 x 10^30341
25,600	1.4370 x 10^30360	1.7238 x 10^30379	2.0942 x 10^30398	2.5767 x 10^30417	3.2109 x 10^30436	4.0523 x 10^30455	5.1796 x 10^30474	6.7052 x 10^30493	8.7913 x 10^30512	1.1674 x 10^30532
25,700	1.5700 x 10^30551	2.1387 x 10^30570	2.9506 x 10^30589	4.1230 x 10^30608	5.8353 x 10^30627	8.3648 x 10^30646	1.2145 x 10^30666	1.7860 x 10^30685	2.6602 x 10^30704	4.0134 x 10^30723
25,800	6.1329 x 10^30742	9.4925 x 10^30761	1.4881 x 10^30781	2.3632 x 10^30800	3.8011 x 10^30819	6.1929 x 10^30838	1.0220 x 10^30858	1.7084 x 10^30877	2.8927 x 10^30896	4.9614 x 10^30915
25,900	8.6198 x 10^30934	1.5169 x 10^30954	2.7042 x 10^30973	4.8832 x 10^30992	8.9323 x 10^31011	1.6551 x 10^31031	3.1066 x 10^31050	5.9069 x 10^31069	1.1377 x 10^31089	2.2199 x 10^31108
26,000	4.3878 x 10^31127	8.7857 x 10^31146	1.7820 x 10^31166	3.6618 x 10^31185	7.6225 x 10^31204	1.6074 x 10^31224	3.4339 x 10^31243	7.4317 x 10^31262	1.6294 x 10^31282	3.6191 x 10^31301
26,100	8.1439 x 10^31320	1.8565 x 10^31340	4.2878 x 10^31359	1.0032 x 10^31379	2.3782 x 10^31398	5.7114 x 10^31417	1.3896 x 10^31437	3.4255 x 10^31456	8.5551 x 10^31475	2.1646 x 10^31495
26,200	5.5493 x 10^31514	1.4413 x 10^31534	3.7928 x 10^31553	1.0112 x 10^31573	2.7316 x 10^31592	7.4764 x 10^31611	2.0732 x 10^31631	5.8252 x 10^31650	1.6583 x 10^31670	4.7834 x 10^31689
26,300	1.3980 x 10^31709	4.1399 x 10^31728	1.2421 x 10^31748	3.7765 x 10^31767	1.1633 x 10^31787	3.6313 x 10^31806	1.1485 x 10^31826	3.6809 x 10^31845	1.1953 x 10^31865	3.9333 x 10^31884
26,400	1.3115 x 10^31904	4.4313 x 10^31923	1.5171 x 10^31943	5.2636 x 10^31962	1.8504 x 10^31982	6.5923 x 10^32001	2.3798 x 10^32021	8.7061 x 10^32040	3.2274 x 10^32060	1.2124 x 10^32080
26,500	4.6158 x 10^32099	1.7807 x 10^32119	6.9620 x 10^32138	2.7583 x 10^32158	1.1075 x 10^32178	4.5064 x 10^32197	1.8582 x 10^32217	7.7657 x 10^32236	3.2889 x 10^32256	1.4116 x 10^32276
26,600	6.1405 x 10^32295	2.7070 x 10^32315	1.2094 x 10^32335	5.4764 x 10^32354	2.5132 x 10^32374	1.1689 x 10^32394	5.5101 x 10^32413	2.6325 x 10^32433	1.2747 x 10^32453	6.2558 x 10^32472
26,700	3.1117 x 10^32492	1.5687 x 10^32512	8.0161 x 10^32531	4.1516 x 10^32551	2.1793 x 10^32571	1.1595 x 10^32591	6.2533 x 10^32610	3.4182 x 10^32630	1.8938 x 10^32650	1.0636 x 10^32670
26,800	6.0545 x 10^32689	3.4935 x 10^32709	2.0432 x 10^32729	1.2113 x 10^32749	7.2795 x 10^32768	4.4343 x 10^32788	2.7381 x 10^32808	1.7138 x 10^32828	1.0874 x 10^32848	6.9941 x 10^32867
26,900	4.5601 x 10^32887	3.0139 x 10^32907	2.0193 x 10^32927	1.3715 x 10^32947	9.4434 x 10^32966	6.5914 x 10^32986	4.6640 x 10^33006	3.3456 x 10^33026	2.4330 x 10^33046	1.7936 x 10^33066
27,000	1.3406 x 10^33086	1.0157 x 10^33106	7.8029 x 10^33125	6.0767 x 10^33145	4.7979 x 10^33165	3.8405 x 10^33185	3.1168 x 10^33205	2.5644 x 10^33225	2.1392 x 10^33245	1.8093 x 10^33265
27,100	1.5514 x 10^33285	1.3488 x 10^33305	1.1890 x 10^33325	1.0626 x 10^33345	9.6295 x 10^33364	8.8475 x 10^33384	8.2423 x 10^33404	7.7855 x 10^33424	7.4566 x 10^33444	7.2412 x 10^33464
27,200	7.1304 x 10^33484	7.1193 x 10^33504	7.2077 x 10^33524	7.3993 x 10^33544	7.7024 x 10^33564	8.1302 x 10^33584	8.7022 x 10^33604	9.4451 x 10^33624	1.0395 x 10^33645	1.1601 x 10^33665
27,300	1.3130 x 10^33685	1.5070 x 10^33705	1.7539 x 10^33725	2.0700 x 10^33745	2.4776 x 10^33765	3.0072 x 10^33785	3.7016 x 10^33805	4.6207 x 10^33825	5.8495 x 10^33845	7.5099 x 10^33865
27,400	9.7781 x 10^33885	1.2911 x 10^33906	1.7291 x 10^33926	2.3484 x 10^33946	3.2348 x 10^33966	4.5191 x 10^33986	6.4030 x 10^34006	9.2013 x 10^34026	1.3410 x 10^34047	1.9824 x 10^34067
27,500	2.9723 x 10^34087	4.5199 x 10^34107	6.9716 x 10^34127	1.0906 x 10^34148	1.7306 x 10^34168	2.7854 x 10^34188	4.5473 x 10^34208	7.5298 x 10^34228	1.2647 x 10^34249	2.1547 x 10^34269
27,600	3.7238 x 10^34289	6.5279 x 10^34309	1.1607 x 10^34330	2.0938 x 10^34350	3.8311 x 10^34370	7.1109 x 10^34390	1.3388 x 10^34411	2.5572 x 10^34431	4.9548 x 10^34451	9.7391 x 10^34471
27,700	1.9419 x 10^34492	3.9282 x 10^34512	8.0611 x 10^34532	1.6782 x 10^34553	3.5443 x 10^34573	7.5943 x 10^34593	1.6508 x 10^34614	3.6406 x 10^34634	8.1456 x 10^34654	1.8490 x 10^34675
27,800	4.2583 x 10^34695	9.9499 x 10^34715	2.3587 x 10^34736	5.6733 x 10^34756	1.3845 x 10^34777	3.4280 x 10^34797	8.6121 x 10^34817	2.1952 x 10^34838	5.6776 x 10^34858	1.4899 x 10^34879
27,900	3.9673 x 10^34899	1.0719 x 10^34920	2.9386 x 10^34940	8.1748 x 10^34960	2.3075 x 10^34981	6.6095 x 10^35001	1.9210 x 10^35022	5.6659 x 10^35042	1.6957 x 10^35063	5.1501 x 10^35083
28,000	1.5872 x 10^35104	4.9642 x 10^35124	1.5755 x 10^35145	5.0747 x 10^35165	1.6587 x 10^35186	5.5021 x 10^35206	1.8522 x 10^35227	6.3278 x 10^35247	2.1939 x 10^35268	7.7201 x 10^35288
28,100	2.7569 x 10^35309	9.9923 x 10^35329	3.6756 x 10^35350	1.3722 x 10^35371	5.1996 x 10^35391	1.9996 x 10^35412	7.8052 x 10^35432	3.0922 x 10^35453	1.2434 x 10^35474	5.0750 x 10^35494
28,200	2.1024 x 10^35515	8.8405 x 10^35535	3.7732 x 10^35556	1.6347 x 10^35577	7.1887 x 10^35597	3.2089 x 10^35618	1.4540 x 10^35639	6.6878 x 10^35659	3.1225 x 10^35680	1.4799 x 10^35701
28,300	7.1205 x 10^35721	3.4777 x 10^35742	1.7243 x 10^35763	8.6791 x 10^35783	4.4347 x 10^35804	2.3004 x 10^35825	1.2114 x 10^35846	6.4769 x 10^35866	3.5155 x 10^35887	1.9371 x 10^35908
28,400	1.0837 x 10^35929	6.1556 x 10^35949	3.5497 x 10^35970	2.0782 x 10^35991	1.2354 x 10^36012	7.4562 x 10^36032	4.5691 x 10^36053	2.8428 x 10^36074	1.7959 x 10^36095	1.1520 x 10^36116
28,500	7.5032 x 10^36136	4.9621 x 10^36157	3.3321 x 10^36178	2.2721 x 10^36199	1.5732 x 10^36220	1.1061 x 10^36241	7.8970 x 10^36261	5.7253 x 10^36282	4.2151 x 10^36303	3.1513 x 10^36324
28,600	2.3925 x 10^36345	1.8446 x 10^36366	1.4443 x 10^36387	1.1484 x 10^36408	9.2739 x 10^36428	7.6055 x 10^36449	6.3345 x 10^36470	5.3581 x 10^36491	4.6030 x 10^36512	4.0161 x 10^36533
28,700	3.5589 x 10^36554	3.2031 x 10^36575	2.9280 x 10^36596	2.7185 x 10^36617	2.5636 x 10^36638	2.4555 x 10^36659	2.3889 x 10^36680	2.3607 x 10^36701	2.3696 x 10^36722	2.4160 x 10^36743
28,800	2.5022 x 10^36764	2.6324 x 10^36785	2.8131 x 10^36806	3.0537 x 10^36827	3.3675 x 10^36848	3.7723 x 10^36869	4.2928 x 10^36890	4.9626 x 10^36911	5.8282 x 10^36932	6.9535 x 10^36953
28,900	8.4282 x 10^36974	1.0378 x 10^36996	1.2983 x 10^37017	1.6501 x 10^37038	2.1308 x 10^37059	2.7955 x 10^37080	3.7262 x 10^37101	5.0463 x 10^37122	6.9437 x 10^37143	9.7077 x 10^37164
29,000	1.3790 x 10^37186	1.9903 x 10^37207	2.9190 x 10^37228	4.3499 x 10^37249	6.5868 x 10^37270	1.0134 x 10^37292	1.5845 x 10^37313	2.5175 x 10^37334	4.0644 x 10^37355	6.6681 x 10^37376
29,100	1.1117 x 10^37398	1.8835 x 10^37419	3.2430 x 10^37440	5.6745 x 10^37461	1.0090 x 10^37483	1.8235 x 10^37504	3.3492 x 10^37525	6.2516 x 10^37546	1.1859 x 10^37568	2.2867 x 10^37589
29,200	4.4811 x 10^37610	8.9252 x 10^37631	1.8068 x 10^37653	3.7177 x 10^37674	7.7752 x 10^37695	1.6528 x 10^37717	3.5713 x 10^37738	7.8440 x 10^37759	1.7512 x 10^37781	3.9742 x 10^37802
29,300	9.1680 x 10^37823	2.1499 x 10^37845	5.1251 x 10^37866	1.2419 x 10^37888	3.0596 x 10^37909	7.6625 x 10^37930	1.9509 x 10^37952	5.0496 x 10^37973	1.3287 x 10^37995	3.5549 x 10^38016
29,400	9.6690 x 10^38037	2.6738 x 10^38059	7.5175 x 10^38080	2.1489 x 10^38102	6.2458 x 10^38123	1.8457 x 10^38145	5.5460 x 10^38166	1.6944 x 10^38188	5.2639 x 10^38209	1.6627 x 10^38231
29,500	5.3410 x 10^38252	1.7445 x 10^38274	5.7942 x 10^38295	1.9569 x 10^38317	6.7215 x 10^38338	2.3476 x 10^38360	8.3389 x 10^38381	3.0122 x 10^38403	1.1065 x 10^38425	4.1341 x 10^38446
29,600	1.5708 x 10^38468	6.0701 x 10^38489	2.3856 x 10^38511	9.5363 x 10^38532	3.8771 x 10^38554	1.6032 x 10^38576	6.7431 x 10^38597	2.8847 x 10^38619	1.2552 x 10^38641	5.5560 x 10^38662
29,700	2.5015 x 10^38684	1.1456 x 10^38706	5.3371 x 10^38727	2.5292 x 10^38749	1.2193 x 10^38771	5.9797 x 10^38792	2.9833 x 10^38814	1.5141 x 10^38836	7.8181 x 10^38857	4.1069 x 10^38879
29,800	2.1948 x 10^38901	1.1934 x 10^38923	6.6018 x 10^38944	3.7157 x 10^38966	2.1278 x 10^38988	1.2397 x 10^39010	7.3501 x 10^39031	4.4337 x 10^39053	2.7214 x 10^39075	1.6997 x 10^39097
29,900	1.0802 x 10^39119	6.9858 x 10^39140	4.5972 x 10^39162	3.0787 x 10^39184	2.0981 x 10^39206	1.4550 x 10^39228	1.0269 x 10^39250	7.3765 x 10^39271	5.3922 x 10^39293	4.0116 x 10^39315

ThatDonGuy

Threads: 122
Posts: 6677

Joined: Jun 22, 2011

January 28th, 2020 at 4:40:05 PM permalink

	0	10	20	30	40	50	60	70	80	90
30,000	3.0375 x 10^39337	2.3408 x 10^39359	1.8360 x 10^39381	1.4657 x 10^39403	1.1909 x 10^39425	9.8499 x 10^39446	8.2920 x 10^39468	7.1055 x 10^39490	6.1978 x 10^39512	5.5030 x 10^39534
30,100	4.9738 x 10^39556	4.5763 x 10^39578	4.2863 x 10^39600	4.0870 x 10^39622	3.9673 x 10^39644	3.9206 x 10^39666	3.9445 x 10^39688	4.0404 x 10^39710	4.2135 x 10^39732	4.4738 x 10^39754
30,200	4.8364 x 10^39776	5.3235 x 10^39798	5.9663 x 10^39820	6.8085 x 10^39842	7.9113 x 10^39864	9.3607 x 10^39886	1.1278 x 10^39909	1.3837 x 10^39931	1.7287 x 10^39953	2.1995 x 10^39975
30,300	2.8498 x 10^39997	3.7603 x 10^40019	5.0531 x 10^40041	6.9156 x 10^40063	9.6391 x 10^40085	1.3683 x 10^40108	1.9784 x 10^40130	2.9135 x 10^40152	4.3700 x 10^40174	6.6765 x 10^40196
30,400	1.0389 x 10^40219	1.6469 x 10^40241	2.6593 x 10^40263	4.3740 x 10^40285	7.3288 x 10^40307	1.2509 x 10^40330	2.1751 x 10^40352	3.8531 x 10^40374	6.9535 x 10^40396	1.2784 x 10^40419
30,500	2.3947 x 10^40441	4.5703 x 10^40463	8.8867 x 10^40485	1.7606 x 10^40508	3.5539 x 10^40530	7.3099 x 10^40552	1.5320 x 10^40575	3.2717 x 10^40597	7.1199 x 10^40619	1.5788 x 10^40642
30,600	3.5679 x 10^40664	8.2167 x 10^40686	1.9283 x 10^40709	4.6121 x 10^40731	1.1242 x 10^40754	2.7928 x 10^40776	7.0713 x 10^40798	1.8248 x 10^40821	4.7996 x 10^40843	1.2867 x 10^40866
30,700	3.5161 x 10^40888	9.7938 x 10^40910	2.7807 x 10^40933	8.0479 x 10^40955	2.3744 x 10^40978	7.1413 x 10^41000	2.1895 x 10^41023	6.8440 x 10^41045	2.1809 x 10^41068	7.0855 x 10^41090
30,800	2.3469 x 10^41113	7.9259 x 10^41135	2.7290 x 10^41158	9.5812 x 10^41180	3.4298 x 10^41203	1.2519 x 10^41226	4.6597 x 10^41248	1.7685 x 10^41271	6.8450 x 10^41293	2.7016 x 10^41316
30,900	1.0874 x 10^41339	4.4635 x 10^41361	1.8685 x 10^41384	7.9777 x 10^41406	3.4738 x 10^41429	1.5428 x 10^41452	6.9886 x 10^41474	3.2289 x 10^41497	1.5217 x 10^41520	7.3153 x 10^41542
31,000	3.5872 x 10^41565	1.7943 x 10^41588	9.1564 x 10^41610	4.7664 x 10^41633	2.5312 x 10^41656	1.3714 x 10^41679	7.5805 x 10^41701	4.2749 x 10^41724	2.4597 x 10^41747	1.4440 x 10^41770
31,100	8.6499 x 10^41792	5.2869 x 10^41815	3.2973 x 10^41838	2.0984 x 10^41861	1.3628 x 10^41884	9.0318 x 10^41906	6.1084 x 10^41929	4.2161 x 10^41952	2.9699 x 10^41975	2.1351 x 10^41998
31,200	1.5666 x 10^42021	1.1732 x 10^42044	8.9686 x 10^42066	6.9976 x 10^42089	5.5730 x 10^42112	4.5306 x 10^42135	3.7598 x 10^42158	3.1852 x 10^42181	2.7546 x 10^42204	2.4321 x 10^42227
31,300	2.1922 x 10^42250	2.0174 x 10^42273	1.8955 x 10^42296	1.8184 x 10^42319	1.7812 x 10^42342	1.7814 x 10^42365	1.8193 x 10^42388	1.8973 x 10^42411	2.0205 x 10^42434	2.1973 x 10^42457
31,400	2.4403 x 10^42480	2.7678 x 10^42503	3.2061 x 10^42526	3.7931 x 10^42549	4.5833 x 10^42572	5.6567 x 10^42595	7.1309 x 10^42618	9.1823 x 10^42641	1.2077 x 10^42665	1.6228 x 10^42688
31,500	2.2274 x 10^42711	3.1234 x 10^42734	4.4744 x 10^42757	6.5485 x 10^42780	9.7919 x 10^42803	1.4959 x 10^42827	2.3351 x 10^42850	3.7245 x 10^42873	6.0702 x 10^42896	1.0109 x 10^42920
31,600	1.7204 x 10^42943	2.9921 x 10^42966	5.3179 x 10^42989	9.6595 x 10^43012	1.7931 x 10^43036	3.4023 x 10^43059	6.5979 x 10^43082	1.3078 x 10^43106	2.6497 x 10^43129	5.4877 x 10^43152
31,700	1.1617 x 10^43176	2.5143 x 10^43199	5.5630 x 10^43222	1.2583 x 10^43246	2.9098 x 10^43269	6.8798 x 10^43292	1.6631 x 10^43316	4.1107 x 10^43339	1.0389 x 10^43363	2.6850 x 10^43386
31,800	7.0959 x 10^43409	1.9177 x 10^43433	5.3001 x 10^43456	1.4981 x 10^43480	4.3307 x 10^43503	1.2804 x 10^43527	3.8721 x 10^43550	1.1977 x 10^43574	3.7896 x 10^43597	1.2265 x 10^43621
31,900	4.0607 x 10^43644	1.3753 x 10^43668	4.7657 x 10^43691	1.6894 x 10^43715	6.1274 x 10^43738	2.2738 x 10^43762	8.6338 x 10^43785	3.3544 x 10^43809	1.3335 x 10^43833	5.4255 x 10^43856
32,000	2.2588 x 10^43880	9.6241 x 10^43903	4.1966 x 10^43927	1.8729 x 10^43951	8.5552 x 10^43974	3.9999 x 10^43998	1.9142 x 10^44022	9.3777 x 10^44045	4.7027 x 10^44069	2.4142 x 10^44093
32,100	1.2688 x 10^44117	6.8277 x 10^44140	3.7614 x 10^44164	2.1217 x 10^44188	1.2254 x 10^44212	7.2473 x 10^44235	4.3890 x 10^44259	2.7219 x 10^44283	1.7287 x 10^44307	1.1244 x 10^44331
32,200	7.4911 x 10^44354	5.1113 x 10^44378	3.5722 x 10^44402	2.5572 x 10^44426	1.8752 x 10^44450	1.4086 x 10^44474	1.0840 x 10^44498	8.5468 x 10^44521	6.9037 x 10^44545	5.7135 x 10^44569
32,300	4.8450 x 10^44593	4.2098 x 10^44617	3.7483 x 10^44641	3.4201 x 10^44665	3.1980 x 10^44689	3.0646 x 10^44713	3.0099 x 10^44737	3.0300 x 10^44761	3.1264 x 10^44785	3.3067 x 10^44809
32,400	3.5850 x 10^44833	3.9846 x 10^44857	4.5401 x 10^44881	5.3037 x 10^44905	6.3522 x 10^44929	7.8007 x 10^44953	9.8226 x 10^44977	1.2683 x 10^45002	1.6793 x 10^45026	2.2803 x 10^45050
32,500	3.1756 x 10^45074	4.5357 x 10^45098	6.6446 x 10^45122	9.9843 x 10^45146	1.5389 x 10^45171	2.4332 x 10^45195	3.9468 x 10^45219	6.5679 x 10^45243	1.1213 x 10^45268	1.9643 x 10^45292
32,600	3.5307 x 10^45316	6.5120 x 10^45340	1.2325 x 10^45365	2.3939 x 10^45389	4.7720 x 10^45413	9.7629 x 10^45437	2.0500 x 10^45462	4.4187 x 10^45486	9.7765 x 10^45510	2.2205 x 10^45535
32,700	5.1775 x 10^45559	1.2394 x 10^45584	3.0462 x 10^45608	7.6875 x 10^45632	1.9920 x 10^45657	5.3007 x 10^45681	1.4485 x 10^45706	4.0650 x 10^45730	1.1716 x 10^45755	3.4686 x 10^45779
32,800	1.0547 x 10^45804	3.2946 x 10^45828	1.0571 x 10^45853	3.4849 x 10^45877	1.1803 x 10^45902	4.1071 x 10^45926	1.4685 x 10^45951	5.3954 x 10^45975	2.0371 x 10^46000	7.9042 x 10^46024
32,900	3.1520 x 10^46049	1.2919 x 10^46074	5.4426 x 10^46098	2.3569 x 10^46123	1.0492 x 10^46148	4.8020 x 10^46172	2.2594 x 10^46197	1.0930 x 10^46222	5.4374 x 10^46246	2.7813 x 10^46271
33,000	1.4630 x 10^46296	7.9148 x 10^46320	4.4037 x 10^46345	2.5201 x 10^46370	1.4834 x 10^46395	8.9827 x 10^46419	5.5956 x 10^46444	3.5861 x 10^46469	2.3646 x 10^46494	1.6043 x 10^46519
33,100	1.1200 x 10^46544	8.0472 x 10^46568	5.9500 x 10^46593	4.5278 x 10^46618	3.5464 x 10^46643	2.8593 x 10^46668	2.3730 x 10^46693	2.0276 x 10^46718	1.7836 x 10^46743	1.6154 x 10^46768
33,200	1.5066 x 10^46793	1.4469 x 10^46818	1.4310 x 10^46843	1.4575 x 10^46868	1.5291 x 10^46893	1.6524 x 10^46918	1.8394 x 10^46943	2.1094 x 10^46968	2.4923 x 10^46993	3.0339 x 10^47018
33,300	3.8056 x 10^47043	4.9190 x 10^47068	6.5524 x 10^47093	8.9956 x 10^47118	1.2729 x 10^47144	1.8566 x 10^47169	2.7916 x 10^47194	4.3273 x 10^47219	6.9158 x 10^47244	1.1396 x 10^47270
33,400	1.9364 x 10^47295	3.3933 x 10^47320	6.1324 x 10^47345	1.1430 x 10^47371	2.1977 x 10^47396	4.3588 x 10^47421	8.9186 x 10^47446	1.8827 x 10^47472	4.1009 x 10^47497	9.2172 x 10^47522
33,500	2.1379 x 10^47548	5.1178 x 10^47573	1.2645 x 10^47599	3.2249 x 10^47624	8.4906 x 10^47649	2.3078 x 10^47675	6.4765 x 10^47700	1.8767 x 10^47726	5.6158 x 10^47751	1.7354 x 10^47777
33,600	5.5391 x 10^47802	1.8261 x 10^47828	6.2191 x 10^47853	2.1880 x 10^47879	7.9537 x 10^47904	2.9874 x 10^47930	1.1595 x 10^47956	4.6509 x 10^47981	1.9281 x 10^48007	8.2623 x 10^48032
33,700	3.6599 x 10^48058	1.6761 x 10^48084	7.9361 x 10^48109	3.8854 x 10^48135	1.9671 x 10^48161	1.0300 x 10^48187	5.5784 x 10^48212	3.1250 x 10^48238	1.8110 x 10^48264	1.0858 x 10^48290
33,800	6.7364 x 10^48315	4.3245 x 10^48341	2.8731 x 10^48367	1.9756 x 10^48393	1.4061 x 10^48419	1.0360 x 10^48445	7.9032 x 10^48470	6.2422 x 10^48496	5.1053 x 10^48522	4.3243 x 10^48548
33,900	3.7935 x 10^48574	3.4472 x 10^48600	3.2450 x 10^48626	3.1648 x 10^48652	3.1982 x 10^48678	3.3491 x 10^48704	3.6347 x 10^48730	4.0886 x 10^48756	4.7675 x 10^48782	5.7632 x 10^48808
34,000	7.2234 x 10^48834	9.3878 x 10^48860	1.2652 x 10^48887	1.7687 x 10^48913	2.5646 x 10^48939	3.8578 x 10^48965	6.0208 x 10^48991	9.7501 x 10^49017	1.6385 x 10^49044	2.8579 x 10^49070
34,100	5.1741 x 10^49096	9.7247 x 10^49122	1.8976 x 10^49149	3.8449 x 10^49175	8.0906 x 10^49201	1.7681 x 10^49228	4.0139 x 10^49254	9.4662 x 10^49280	2.3195 x 10^49307	5.9059 x 10^49333
34,200	1.5628 x 10^49360	4.2983 x 10^49386	1.2289 x 10^49413	3.6528 x 10^49439	1.1289 x 10^49466	3.6287 x 10^49492	1.2130 x 10^49519	4.2179 x 10^49545	1.5258 x 10^49572	5.7429 x 10^49598
34,300	2.2493 x 10^49625	9.1692 x 10^49651	3.8905 x 10^49678	1.7185 x 10^49705	7.9037 x 10^49731	3.7852 x 10^49758	1.8880 x 10^49785	9.8091 x 10^49811	5.3091 x 10^49838	2.9940 x 10^49865
34,400	1.7595 x 10^49892	1.0776 x 10^49919	6.8804 x 10^49945	4.5796 x 10^49972	3.1783 x 10^49999	2.3003 x 10^50026	1.7365 x 10^50053	1.3674 x 10^50080	1.1235 x 10^50107	9.6321 x 10^50133
34,500	8.6185 x 10^50160	8.0494 x 10^50187	7.8487 x 10^50214	7.9909 x 10^50241	8.4963 x 10^50268	9.4357 x 10^50295	1.0947 x 10^50323	1.3270 x 10^50350	1.6810 x 10^50377	2.2257 x 10^50404
34,600	3.0806 x 10^50431	4.4582 x 10^50458	6.7468 x 10^50485	1.0679 x 10^50513	1.7682 x 10^50540	3.0635 x 10^50567	5.5541 x 10^50594	1.0539 x 10^50622	2.0936 x 10^50649	4.3548 x 10^50676
34,700	9.4859 x 10^50703	2.1643 x 10^50731	5.1733 x 10^50758	1.2957 x 10^50786	3.4012 x 10^50813	9.3588 x 10^50840	2.6999 x 10^50868	8.1681 x 10^50895	2.5918 x 10^50923	8.6278 x 10^50950
34,800	3.0136 x 10^50978	1.1047 x 10^51006	4.2512 x 10^51033	1.7176 x 10^51061	7.2877 x 10^51088	3.2479 x 10^51116	1.5207 x 10^51144	7.4826 x 10^51171	3.8697 x 10^51199	2.1039 x 10^51227
34,900	1.2028 x 10^51255	7.2324 x 10^51282	4.5750 x 10^51310	3.0452 x 10^51338	2.1334 x 10^51366	1.5734 x 10^51394	1.2218 x 10^51422	9.9941 x 10^51449	8.6117 x 10^51477	7.8193 x 10^51505
35,000	7.4833 x 10^51533	7.5504 x 10^51561	8.0335 x 10^51589	9.0159 x 10^51617	1.0675 x 10^51646	1.3340 x 10^51674	1.7597 x 10^51702	2.4510 x 10^51730	3.6055 x 10^51758	5.6035 x 10^51786
35,100	9.2027 x 10^51814	1.5975 x 10^51843	2.9323 x 10^51871	5.6924 x 10^51899	1.1690 x 10^51928	2.5407 x 10^51956	5.8449 x 10^51984	1.4237 x 10^52013	3.6732 x 10^52041	1.0040 x 10^52070
35,200	2.9085 x 10^52098	8.9322 x 10^52126	2.9089 x 10^52155	1.0049 x 10^52184	3.6837 x 10^52212	1.4333 x 10^52241	5.9216 x 10^52269	2.5985 x 10^52298	1.2115 x 10^52327	6.0038 x 10^52355
35,300	3.1632 x 10^52384	1.7726 x 10^52413	1.0568 x 10^52442	6.7062 x 10^52470	4.5308 x 10^52499	3.2603 x 10^52528	2.4996 x 10^52557	2.0427 x 10^52586	1.7798 x 10^52615	1.6542 x 10^52644
35,400	1.6406 x 10^52673	1.7369 x 10^52702	1.9637 x 10^52731	2.3719 x 10^52760	3.0618 x 10^52789	4.2260 x 10^52818	6.2389 x 10^52847	9.8561 x 10^52876	1.6668 x 10^52906	3.0191 x 10^52935
35,500	5.8592 x 10^52964	1.2189 x 10^52994	2.7192 x 10^53023	6.5087 x 10^53052	1.6722 x 10^53082	4.6137 x 10^53111	1.3676 x 10^53141	4.3577 x 10^53170	1.4932 x 10^53200	5.5055 x 10^53229
35,600	2.1851 x 10^53259	9.3408 x 10^53288	4.3027 x 10^53318	2.1369 x 10^53348	1.1448 x 10^53378	6.6193 x 10^53407	4.1331 x 10^53437	2.7884 x 10^53467	2.0337 x 10^53497	1.6045 x 10^53527
35,700	1.3700 x 10^53557	1.2669 x 10^53587	1.2695 x 10^53617	1.3792 x 10^53647	1.6258 x 10^53677	2.0804 x 10^53707	2.8918 x 10^53737	4.3694 x 10^53767	7.1811 x 10^53797	1.2845 x 10^53828
35,800	2.5026 x 10^53858	5.3142 x 10^53888	1.2307 x 10^53919	3.1110 x 10^53949	8.5892 x 10^53979	2.5920 x 10^54010	8.5563 x 10^54040	3.0918 x 10^54071	1.2240 x 10^54102	5.3127 x 10^54132
35,900	2.5303 x 10^54163	1.3234 x 10^54194	7.6078 x 10^54224	4.8108 x 10^54255	3.3493 x 10^54286	2.5696 x 10^54317	2.1743 x 10^54348	2.0310 x 10^54379	2.0964 x 10^54410	2.3933 x 10^54441
36,000	3.0248 x 10^54472	4.2366 x 10^54503	6.5825 x 10^54534	1.1357 x 10^54566	2.1781 x 10^54597	4.6487 x 10^54628	1.1053 x 10^54660	2.9309 x 10^54691	8.6779 x 10^54722	2.8721 x 10^54754
36,100	1.0638 x 10^54786	4.4159 x 10^54817	2.0564 x 10^54849	1.0758 x 10^54881	6.3309 x 10^54912	4.1962 x 10^54944	3.1370 x 10^54976	2.6487 x 10^55008	2.5297 x 10^55040	2.7367 x 10^55072
36,200	3.3587 x 10^55104	4.6835 x 10^55136	7.4320 x 10^55168	1.3442 x 10^55201	2.7761 x 10^55233	6.5567 x 10^55265	1.7742 x 10^55298	5.5103 x 10^55330	1.9678 x 10^55363	8.0963 x 10^55395
36,300	3.8451 x 10^55428	2.1121 x 10^55461	1.3447 x 10^55494	9.9439 x 10^55526	8.5596 x 10^55559	8.5961 x 10^55592	1.0095 x 10^55626	1.3896 x 10^55659	2.2480 x 10^55692	4.2843 x 10^55725
36,400	9.6447 x 10^55758	2.5716 x 10^55792	8.1449 x 10^55825	3.0730 x 10^55859	1.3853 x 10^55893	7.4860 x 10^55926	4.8643 x 10^55960	3.8136 x 10^55994	3.6200 x 10^56028	4.1756 x 10^56062
36,500	5.8748 x 10^56096	1.0121 x 10^56131	2.1439 x 10^56165	5.6076 x 10^56199	1.8190 x 10^56234	7.3520 x 10^56268	3.7202 x 10^56303	2.3688 x 10^56338	1.9079 x 10^56373	1.9546 x 10^56408
36,600	2.5619 x 10^56443	4.3222 x 10^56478	9.4462 x 10^56513	2.6924 x 10^56549	1.0079 x 10^56585	4.9938 x 10^56620	3.3000 x 10^56656	2.9332 x 10^56692	3.5383 x 10^56728	5.8472 x 10^56764
36,700	1.3371 x 10^56801	4.2771 x 10^56837	1.9356 x 10^56874	1.2547 x 10^56911	1.1804 x 10^56948	1.6348 x 10^56985	3.3846 x 10^57022	1.0650 x 10^57060	5.1862 x 10^57097	3.9861 x 10^57135
36,800	4.9412 x 10^57173	1.0115 x 10^57212	3.5107 x 10^57250	2.1267 x 10^57289	2.3232 x 10^57328	4.7467 x 10^57367	1.8908 x 10^57407	1.5398 x 10^57447	2.7075 x 10^57487	1.0956 x 10^57528
36,900	1.1003 x 10^57569	3.0018 x 10^57610	2.4848 x 10^57652	7.1657 x 10^57694	8.6000 x 10^57737	5.4455 x 10^57781	2.5376 x 10^57826	1.4369 x 10^57872	2.3017 x 10^57919	6.0122 x 10^57968
37,000	2.9093 x 10^58023

weezrDASvegas

Threads: 2
Posts: 69

Joined: Feb 2, 2018

January 29th, 2020 at 3:09:49 AM permalink

Quote: ThatDonGuy
Quote: weezrDASvegas
Quote: ThatDonGuy
It's not that hard; I get 1 in 78.2.

Here's how:
The probability of getting 1000, say, zeroes in 37,000 spins of a single-zero wheel is (37,000)C(1000) x (1/37)¹⁰⁰⁰ x (36/37)^36,000
Most methods of calculating this would result in arithmetic overflows, but if you use logarithms and a spreadsheet, you can do it.

(37,000)C(1000) = 37,000 / 1 x 36,999 / 2 x 36,998 / 3 x ... x 36,002 / 999 x 36,001 / 1000
log ((37,000)C(1000)) = log 37,000 - log 1 + log 36,999 - log 2 + ... + log 36,001 - log 1000

(1/37)¹⁰⁰⁰ x (36/37)^36,000 = 36^36,000 / 37^37,000
log ((1/37)¹⁰⁰⁰ x (36/37)^36,000) = 36,000 log 36 - 37,000 log 37

log ((37,000)C(1000) x (1/37)¹⁰⁰⁰ x (36/37)^36,000) = log ((37,000)C(1000)) + log (1/37)¹⁰⁰⁰ x (36/37)^36,000)
= log 37,000 - log 1 + log 36,999 - log 2 + ... + log 36,001 - log 1000 + 36,000 log 36 - 37,000 log 37

(37,000)C(1000) x (1/37)¹⁰⁰⁰ x (36/37)^36,000 = 10 to the power of (log 37,000 - log 1 + log 36,999 - log 2 + ... + log 36,001 - log 1000 + 36,000 log 36 - 37,000 log 37) = about 1 / 78.19456.

�log ((37,000)C(1000) x (1/37)1000 x (36/37)36,000) = log ((37,000)C(1000)) + log (1/37)1000 x (36/37)36,000)
= log 37,000 - log 1 + log 36,999 - log 2 + ... + log 36,001 - log 1000 + 36,000 log 36 - 37,000 log 37

(37,000)C(1000) x (1/37)1000 x (36/37)36,000 = 10 to the power of (log 37,000 - log 1 + log 36,999 - log 2 + ... + log 36,001 - log 1000 + 36,000 log 36 - 37,000 log 37) = about 1 / 78.19456.�
Boy, oh, boy!!!

REPEAT
THE FORMULA IN SANE MATHS IS ONLY ONE

BDF = C(N, M) * p^M * (1 � p)^(N � M)

There aint nothing else around this formula for M SUCCESSES IN N TRIALS, where M<=N
Correct - and that's what I used,
C(37,000, 1000) * (1/37)^1000 * (36/37)^36,000 = about 1 / 78.19456.
However, if you try calculating this, you get some incredibly large numbers - for example:
C(37,000, 1000) =    479,276,699,178,809
,649,854,007,516,573,731,742,327,273,069
,805,016,086,657,405,455,109,799,606,702
,488,074,316,078,886,738,673,405,423,536
,935,995,180,640,134,170,351,203,927,583
,441,073,501,450,606,034,739,281,380,081
,266,971,643,546,937,157,336,662,888,922
,253,691,906,080,498,872,891,827,810,260
,123,627,597,442,890,261,235,017,526,349
,206,317,513,740,605,712,640,017,265,142
,974,688,761,487,034,690,463,696,780,162
,215,085,889,685,494,249,490,525,236,409
,469,240,814,649,833,608,046,768,129,786
,581,489,455,386,273,747,686,446,966,729
,405,118,683,652,656,515,783,092,956,219
,134,045,074,789,599,756,927,735,827,596
,658,822,553,856,917,516,397,236,435,813
,161,723,188,024,710,387,951,880,112,301
,158,825,892,566,463,810,963,013,768,882
,817,406,866,641,260,587,584,829,999,008
,147,384,380,458,874,009,596,572,030,879
,848,117,282,525,969,342,809,054,946,839
,342,858,681,545,894,890,490,336,636,103
,689,016,433,539,011,047,886,984,785,468
,380,720,407,098,050,506,787,090,587,675
,922,007,973,537,988,719,106,628,037,637
,201,188,379,455,839,387,495,776,823,185
,949,485,546,344,041,897,490,449,177,307
,306,200,622,994,704,372,960,416,193,336
,688,308,713,514,327,058,685,135,578,804
,394,060,159,144,923,559,645,007,689,684
,251,222,486,397,584,028,502,937,082,204
,358,533,104,641,877,406,718,240,282,261
,782,869,775,064,983,145,093,871,815,047
,611,226,716,711,985,847,297,826,933,578
,822,811,723,698,508,244,220,268,746,362
,471,556,340,712,370,272,754,537,463,366
,470,328,884,897,135,476,737,821,874,244
,866,467,383,847,786,965,458,952,998,588
,646,202,234,696,643,914,331,164,731,120
,696,118,602,946,955,042,436,415,360,583
,800,119,156,026,077,108,210,288,200,171
,543,780,460,665,972,025,328,483,787,834
,834,326,609,687,380,472,280,261,337,876
,258,947,467,008,777,949,621,986,484,591
,629,806,072,515,626,901,321,190,886,205
,758,970,285,393,041,086,834,041,780,080
,097,257,762,255,249,024,777,235,192,639
,390,351,457,284,466,347,596,327,472,028
,526,176,040,029,776,609,721,789,662,742
,918,233,956,273,583,373,632,927,934,549
,338,501,441,407,809,662,581,088,983,489
,387,476,400,674,188,551,714,927,652,671
,236,973,901,796,994,054,803,975,272,026
,083,124,171,733,928,272,977,188,321,254
,479,149,728,028,229,308,027,858,103,509
,046,658,217,579,332,379,673,689,007,685
,023,992,631,412,835,356,783,313,694,401
,502,082,353,166,957,744,010,576,726,927
,867,927,846,209,737,291,572,878,147,601
,030,873,362,980,407,225,271,549,165,836
,099,653,929,007,468,378,098,599,877,215
,417,732,947,321,440,475,756,911,637,413
,002,847,727,410,003,441,734,525,421,999
,551,574,325,706,603,163,072,805,655,372
,445,389,579,976,492,590,483,756,353,780
,275,903,959,095,519,952,117,190,925,440
That's a 1995-digit number
However, if you note a few things, it makes calculating it simpler:
10^(log N) = N
log (A * B) = log A + log B
log (A^B) = B log A

Let P be the value we are trying to calculate
P = C(37,000, 1000) * (1/37)^1000 * (36/37)^36,000
As shown in that spoiler box, C(37,000, 1000) = about 4.79277 * 10^1994
(1/37)^1000 = 1 / (37^1000), and (36/37)^36,000 = (36^36,000) / (37^36,000)
(1/37)^1000 * (36/37)^36,000 = (36^36,000) / (37^37,000)
So P = C(37,000, 1000) * (36^36,000) / (37^37,000)

log P = log (C(37,000, 1000) * (36^36,000) / (37^37,000))
= log (4.79277 * 10^1994) + log (36^36,000) - log (37^37,000)
= log 4.79277 + log (10^1994) + log (36^36,000) - log (37^37,000)
= 0.6806 + 1994 + 36,000 log (36) - 37,000 log (37)
= -1.8931763

P = 10^(log P) = 10^(-1.8931763) = about 1 / 78.1945.
Got it?

Also, some quick computing shows that 10^1058 is approximately the probability of zero coming up 3834 times in 37,000 spins.

Many dispute the accuracy of extremely large numbers like in your posts. what libraries you using and why you trust them? and whats the probability of exactly 500 heads in 1000 cointosses according to your algorithm?

your first algo was different� very long starting with log1 ending with log(1000) and had 1000 steps working with extremely long numbers�

(37,000)C(1000) = 37,000 / 1 x 36,999 / 2 x 36,998 / 3 x ... x 36,002 / 999 x 36,001 / 1000
log ((37,000)C(1000)) = log 37,000 - log 1 + log 36,999 - log 2 + ... + log 36,001 - log 1000

Also, some quick computing shows that 10^1058 is approximately the probability of zero coming up 3834 times in 37,000 spins.

10^1058 is a very large number.. way above 1 probability is between 0 and 1.

we talkin here probability of EXACTLY, right? like I sez above
* probability EXACTLY 500 successes in 1000 trials: 2.5% (you might figure 50%) � but
* probability AT LEAST 500 successes in 1000 trials: 51.3%
* probability AT MOST 500 successes in 1000 trials: 51.3%.

ThatDonGuy