Prime Numbers: I don't get it
July 18th, 2018 at 5:43:32 PM
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I don't get the fascination with prime numbers, and just came across this:
Oliver Sacks in his book Uncle Tungsten writes about prime numbers that he as a youngster"... loved the fact that they were indivisible, could not be broken down, were inalienable themselves... Primes were the building blocks of all other numbers" He was obsessed with finding a pattern, a logic to them, he says.
I just don't get it. I 'get it' with some fascinations with numbers, that logarithms actually work astounds me for instance. I just don't get the fascination with prime numbers. Indivisible? Meh, so what.
I do 'get it' that it is a good sign of mathematical aptitude to have such fascination, which helps explain my lack of it.
Oliver Sacks in his book Uncle Tungsten writes about prime numbers that he as a youngster"... loved the fact that they were indivisible, could not be broken down, were inalienable themselves... Primes were the building blocks of all other numbers" He was obsessed with finding a pattern, a logic to them, he says.
I just don't get it. I 'get it' with some fascinations with numbers, that logarithms actually work astounds me for instance. I just don't get the fascination with prime numbers. Indivisible? Meh, so what.
I do 'get it' that it is a good sign of mathematical aptitude to have such fascination, which helps explain my lack of it.
the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: “Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell!” She is, after all, stone deaf. ... Arnold Snyder
July 18th, 2018 at 5:59:08 PM
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For one, modern encryption is based the fact that you can multiply two prime numbers to get a much larger prime number, with no way for a computer to calculate what two primes that were originally multiplied.
There definitely other interesting properties of prime numbers, but that’s all I have on the tip of my tongue.
There definitely other interesting properties of prime numbers, but that’s all I have on the tip of my tongue.
Last edited by: gamerfreak on Jul 18, 2018
July 18th, 2018 at 6:03:32 PM
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Quote: gamerfreakFor one, modern encryption is based the fact that you can multiply two prime numbers to get a much larger prime number, with no way for a computer to calculate what two primes were originally multiplied.
I am missing something here. If you multiply 2 numbers don't you by definition get a non-prime number?
3x5=15
7x11=77
I know they use primes for encryption, but something seems wrong the way I am reading this.
All animals are equal, but some are more equal than others
July 18th, 2018 at 6:06:56 PM
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Quote: AZDuffmanI am missing something here. If you multiply 2 numbers don't you by definition get a non-prime number?
3x5=15
7x11=77
I know they use primes for encryption, but something seems wrong the way I am reading this.
My fault, the product of two prime numbers is non-prime.
Same concept though. Multiply 2 large primes and it’s very difficult to factor the result.
July 18th, 2018 at 6:45:07 PM
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In RSA, for example, the larger number in the public key is the product of two prime numbers.
However, I think odiusgambit's "problem" is with people who think that we need to know, for example, that the sum of the reciprocals of the prime numbers does not converge to a finite number.
Still, prime numbers are useful in mathematics; for example, they form the basis of the Fundamental Theorem of Arithmetic (an integer > 1 that is not prime has exactly one set of prime numbers whose product is that number - for example, 2 x 2 x 3 x 5 = 60; there is no other set of prime numbers whose product is 60), which is used to show that all square roots of numbers that are not perfect squares are irrational.
However, I think odiusgambit's "problem" is with people who think that we need to know, for example, that the sum of the reciprocals of the prime numbers does not converge to a finite number.
Still, prime numbers are useful in mathematics; for example, they form the basis of the Fundamental Theorem of Arithmetic (an integer > 1 that is not prime has exactly one set of prime numbers whose product is that number - for example, 2 x 2 x 3 x 5 = 60; there is no other set of prime numbers whose product is 60), which is used to show that all square roots of numbers that are not perfect squares are irrational.
July 18th, 2018 at 7:19:41 PM
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Sorry kinda laughed when gamerfreak said product of two primes is prime, with a strike through. :)
<insert Chinese man with hands on his head dot gif>
Sorry I don’t have anything exceptionally interesting about primes. Well, other than a pretty interesting sequence of pattern if you sum primes (2, 2+3, 2+3+5, 2+3+5+7....).
<insert Chinese man with hands on his head dot gif>
Sorry I don’t have anything exceptionally interesting about primes. Well, other than a pretty interesting sequence of pattern if you sum primes (2, 2+3, 2+3+5, 2+3+5+7....).
July 18th, 2018 at 7:27:46 PM
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I think Nathan needs to get over to this thread for some hot lotto picks. She will be seeing all kinds of choices.
July 18th, 2018 at 7:58:37 PM
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1-800-GAMBLER, which is 18004262537, is the product of two 6-digit primes.
You can find them using Wolfram Alpha.
You can find them using Wolfram Alpha.
July 18th, 2018 at 8:04:45 PM
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Quote: ChesterDog1-800-GAMBLER, which is 18004262537, is the product of two 6-digit primes.
You can find them using Wolfram Alpha.
Nice pun.
Quote:two 6-digit
Quote:two 6
Quote:2 6
Quote:26
Quote:product of two primes
Coincidence? You decide.
July 19th, 2018 at 3:09:18 AM
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ODG is Nathan.
I am a robot.
July 19th, 2018 at 7:59:11 AM
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I love prime numbers. Beautiful, useful, and mysterious. It give me joy to see them in everyday life, like the amount something costs after tax is a prime number. The pursuit of prime numbers is bittersweet as there is so much we don't know about them, yet the answers seem strangely just out of reach. I'd like to close with this sermon from the church of mathology.
Direct: https://www.youtube.com/watch?v=iJvMSitW80s
Direct: https://www.youtube.com/watch?v=iJvMSitW80s
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
July 19th, 2018 at 8:21:54 AM
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I have a much stronger affection for highly composite numbers. Like how 12 has seven factors. In base 10 kids learn how to count by 1, 2, 5, and 10 in kindergarten. If we had base 12, they could learn to count by 1, 2, 3, 4, 6, 8, 9, and 12 by about the same age. That ability would make people much stronger at math in early years, which would also make people stronger at math throughout our entire lives.
36 is both a square and a triangle. That's more interesting than 37.
36 is both a square and a triangle. That's more interesting than 37.
July 19th, 2018 at 9:22:35 AM
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Quote: odiousgambitI don't get the fascination with prime numbers, and just came across this:
Oliver Sacks in his book Uncle Tungsten writes about prime numbers that he as a youngster"... loved the fact that they were indivisible, could not be broken down, were inalienable themselves... Primes were the building blocks of all other numbers" He was obsessed with finding a pattern, a logic to them, he says.
I just don't get it. I 'get it' with some fascinations with numbers, that logarithms actually work astounds me for instance. I just don't get the fascination with prime numbers. Indivisible? Meh, so what.
I do 'get it' that it is a good sign of mathematical aptitude to have such fascination, which helps explain my lack of it.
How about illegal prime #s?
https://wizardofvegas.com/forum/off-topic/general/31128-illegal-prime/
Craps is paradise (Pair of dice).
Lets hear it for the SpeedCount Mathletes :)
July 19th, 2018 at 2:02:56 PM
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this is an example of a few of the numbers I run before deciding which horse to bet on:
the foolish sayings of a rich man often pass for words of wisdom by the fools around him
July 19th, 2018 at 6:51:56 PM
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Quote: 100xOdds
How about illegal prime #s?
https://wizardofvegas.com/forum/off-topic/general/31128-illegal-prime/
I read that as “Illegal Prine”.
A falling knife has no handle.
July 19th, 2018 at 7:08:26 PM
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I’m not a math guy, but I could have been. The thing about primes that fascinates me is that there are exactly as many as are needed to keep generating numbers. All the numbers that aren’t prime depend on primes. Every single one. Doesn’t matter how big.
It ties into the truth that numbers aren’t real things; they are representations of reality. You can say that you have five batteries, but what you really have is batteries. Five is a measurement that attaches to the fact.
It’s all inside your head.
Propel, propel, propel your craft
Softly through liquid solution.
Ecstatically, ecstatically, ecstatically, ecstatically
Existence is but an illusion.
It ties into the truth that numbers aren’t real things; they are representations of reality. You can say that you have five batteries, but what you really have is batteries. Five is a measurement that attaches to the fact.
It’s all inside your head.
Propel, propel, propel your craft
Softly through liquid solution.
Ecstatically, ecstatically, ecstatically, ecstatically
Existence is but an illusion.
A falling knife has no handle.
July 19th, 2018 at 7:50:10 PM
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Quote: MoscaIt ties into the truth that numbers aren’t real things; they are representations of reality. You can say that you have five batteries, but what you really have is batteries. Five is a measurement that attaches to the fact.
It’s all inside your head.
I always say that when there is a thread that is based on some paradox involving infinity. There really is no such thing as infinity in real life.
Anyway, I see great beauty, even existence of a higher power, when I look at things like the Taylor expansion, or how so many infinite series lead to some function of pi or e. That can't be just inside my head. Or maybe it can be.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
July 19th, 2018 at 7:57:16 PM
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Quote: WizardI always say that when there is a thread that is based on some paradox involving infinity. There really is no such thing as infinity in real life.
Anyway, I see great beauty, even existence of a higher power, when I look at things like the Taylor expansion, or how so many infinite series lead to some function of pi or e. That can't be just inside my head. Or maybe it can be.
I agree. It is the kind of beauty that you almost have to look away from: blinding in its perfection, but only a small insignificant part of the large picture... letting you know there IS a larger picture, but giving no further clue what that picture might look like, only hints.
And don’t even get me started on analog and digital. Because we live in analog, but at its most basic level the world is digital.
A falling knife has no handle.
July 19th, 2018 at 8:13:02 PM
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July 20th, 2018 at 4:20:26 AM
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Yet, when we are talking about numbers, there is no way you can put an upper limit on what the largest number can be.Quote: WizardI always say that when there is a thread that is based on some paradox involving infinity. There really is no such thing as infinity in real life.
the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: “Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell!” She is, after all, stone deaf. ... Arnold Snyder
July 20th, 2018 at 6:19:59 AM
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I heard him lecture and thought he was a nice guy. I won't say I was fascinated by prime numbers in school but I did try to determine relationships between them and try to derive a rule for detecting the next one.Quote: ChesterDogYou can find them using Wolfram Alpha.
July 20th, 2018 at 8:15:12 AM
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Quote: FleaStiff...in school but I did try to determine relationships between them and try to derive a rule for detecting the next one.
That is probably the biggest mystery in prime numbers, finding the "next one," other than by brute force.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
July 20th, 2018 at 10:35:11 AM
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Numbers arise from a physical reality: a need to count objects (or physical particles).
When you have a number of objects, such as rocks or people, that cannot be divided into multiple equal-sized batches, then you will find that the number of your objects is a prime number.
Ex: 21 potatoes can be divided into 7 batches each of 3 potatoes or 3 batches of 7 each. But 23 potatoes cannot be divided into any number of equal sized batches because 23 is a prime number.
That's a very practical real-life definition of a prime number that would have been meaningful to prehistoric man.
Now, every natural number can be written as a product of primes (including, by definition, a single prime) such as
120 =2*2*2*3*5 or 23*3*5
11 = 11
and, importantly, every such product of primes corresponds uniquely to a natural number.
So, you could make a case that we don't need composite numbers at all to count, all we need are primes (and 1) such as:
1, 2, 3, 2*2, 5, 3*2, 7, 2*2*2, 3*3, 2*5, 11, 2*2*3, 13, 2*7, 3*5, . . .
With this set of definitions, we have dispensed with >55% of all numbers. To me, prime numbers have the appeal of seeming like a more fundamental "number system."
When you have a number of objects, such as rocks or people, that cannot be divided into multiple equal-sized batches, then you will find that the number of your objects is a prime number.
Ex: 21 potatoes can be divided into 7 batches each of 3 potatoes or 3 batches of 7 each. But 23 potatoes cannot be divided into any number of equal sized batches because 23 is a prime number.
That's a very practical real-life definition of a prime number that would have been meaningful to prehistoric man.
Now, every natural number can be written as a product of primes (including, by definition, a single prime) such as
120 =2*2*2*3*5 or 23*3*5
11 = 11
and, importantly, every such product of primes corresponds uniquely to a natural number.
So, you could make a case that we don't need composite numbers at all to count, all we need are primes (and 1) such as:
1, 2, 3, 2*2, 5, 3*2, 7, 2*2*2, 3*3, 2*5, 11, 2*2*3, 13, 2*7, 3*5, . . .
With this set of definitions, we have dispensed with >55% of all numbers. To me, prime numbers have the appeal of seeming like a more fundamental "number system."
Last edited by: gordonm888 on Jul 20, 2018
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
July 20th, 2018 at 3:42:49 PM
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Yeah, azzackly! That's what I meant when I said that there are exactly as many as are needed to keep generating numbers.
A falling knife has no handle.
July 20th, 2018 at 3:47:01 PM
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What does the spacing of primes tell us about larger numbers?
A falling knife has no handle.
July 20th, 2018 at 5:00:28 PM
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Quote: gordonm888With this set of definitions, we have dispensed with >55% of all numbers. To me, prime numbers have the appeal of seeming like a more fundamental "number system."
Haven't we dispensed with many more than that? The Prime Number Theorem suggests the ratio of prime numbers under a google is approximately 1/ln(10^100) = 0.004342945. We could get into the Riemann hypothesis for a more accurate estimate, but I don't think I could match wits with you on that.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
July 20th, 2018 at 8:27:44 PM
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Quote: ChesterDog1-800-GAMBLER, which is 18004262537, is the product of two 6-digit primes.
You can find them using Wolfram Alpha.
Holy crap, what are the odds of that?!?! Bad joke for that number. :P Did you stumble across that yourself, or read it from somewhere else?
July 20th, 2018 at 8:38:50 PM
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Quote: odiousgambitYet, when we are talking about numbers, there is no way you can put an upper limit on what the largest number can be.
There's also no limit on what the largest prime number can be
Assume there is a largest prime number; call it P.
Let N = P! + 1.
If you divide N by any integer from 2 to P, you get a remainder of 1, so N has no prime factors less than P.
This means that either N is prime, or all of its prime factors > P.
In either case, there must exist at least one prime number > P, so P is not the largest prime.
July 20th, 2018 at 10:05:24 PM
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Quote: ThatDonGuyThere's also no limit on what the largest prime number can be
Assume there is a largest prime number; call it P.
Let N = P! + 1.
If you divide N by any integer from 2 to P, you get a remainder of 1, so N has no prime factors less than P.
This means that either N is prime, or all of its prime factors > P.
In either case, there must exist at least one prime number > P, so P is not the largest prime.
Is this something you already knew and/or were taught....or did you just come up with this proof on the fly?
July 21st, 2018 at 8:58:32 AM
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Quote: RSQuote: ThatDonGuyThere's also no limit on what the largest prime number can be
Assume there is a largest prime number; call it P.
Let N = P! + 1.
If you divide N by any integer from 2 to P, you get a remainder of 1, so N has no prime factors less than P.
This means that either N is prime, or all of its prime factors > P.
In either case, there must exist at least one prime number > P, so P is not the largest prime.
Is this something you already knew and/or were taught....or did you just come up with this proof on the fly?
Something I already knew. In fact, it's usually one of the first things "primeophiles" learn.
Now, whether or not there is a largest number N such that both N - 1 and N + 1 are prime is one of the "great unsolved questions of mathematics."
July 21st, 2018 at 11:16:20 AM
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Quote: WizardHaven't we dispensed with many more than that? The Prime Number Theorem suggests the ratio of prime numbers under a google is approximately 1/ln(10^100) = 0.004342945. We could get into the Riemann hypothesis for a more accurate estimate, but I don't think I could match wits with you on that.
LOL, yes, I remembered it vaguely as .43%. I meant to write "more than 99.55%" and was going to check on the actual number but wound up hitting Send because of some real-life circumstance. Thanks for correcting this awful misstatement Still, my point was (and I know you agree) that prime numbers are not some silly artifact such as 'numbers that are palindromes in base 10'. Prime seem like they are fundamentally important.
Last edited by: gordonm888 on Jul 21, 2018
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
July 21st, 2018 at 1:56:34 PM
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Quote: gordonm888Prime seem like they are fundamentally important.
I agree 100%!
Who knows what this ?
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
July 21st, 2018 at 2:30:26 PM
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ulam spiral. I didn't know, but google image search is maybe one of the greatest tools of our time. Took literally 2 clicks and 2 seconds to get the answer.
Psalm 25:16
Turn to me and be gracious to me, for I am lonely and afflicted.
Proverbs 18:2
A fool finds no satisfaction in trying to understand, for he would rather express his own opinion.
July 21st, 2018 at 2:40:22 PM
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(without internet searching) I believe it is a plot of the frequency of primes as represented by dark spots on a spiral grid, where blank spots represent composite numbers. This was originally an attempt by a mathematician to look for unexpected patterns in the sequence of primes. The origin of the plot is visually identifiable by a higher density of primes, which I believe is at the center of the image.
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
July 21st, 2018 at 2:43:49 PM
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Quote: gordonm888(without internet searching) I believe it is a plot of the frequency of primes as represented by dark spots on a spiral grid, where blank spots represent composite numbers. This was originally an attempt by a mathematician to look for unexpected patterns in the sequence of primes. The origin of the plot is visually identifiable by a higher density of primes, which I believe is at the center of the image.
Yes! Note how lots of primes fall on a diagonal line. It goes to show, I think, that there is some order in the seemingly random world of primes.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
July 21st, 2018 at 8:27:33 PM
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Freakiest thing about that spiral is there is absolutely no known reason for those diagonal lines to exist
July 22nd, 2018 at 4:05:40 AM
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Quote: WizardQuote: gordonm888(without internet searching) I believe it is a plot of the frequency of primes as represented by dark spots on a spiral grid, where blank spots represent composite numbers. This was originally an attempt by a mathematician to look for unexpected patterns in the sequence of primes. The origin of the plot is visually identifiable by a higher density of primes, which I believe is at the center of the image.
Yes! Note how lots of primes fall on a diagonal line. It goes to show, I think, that there is some order in the seemingly random world of primes.
It makes our minds appear insufficient, that we can only conceive of numbers linearly, when to some other higher intelligence the answer must be as obvious as a child’s pegboard.
A falling knife has no handle.
