Greasyjohn
Greasyjohn
Joined: Dec 8, 2013
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December 16th, 2013 at 3:41:12 PM permalink
Thanks everyone for your replies. I have the book One Two Three Infinity and just love this stuff. I had thought that what was being stated ( which I didn't grasp) was that if you multiply primes ie, 2x3x5x7x11x13 etc., that the answer you get after any multiplication (plus one) is a prime. But when you get to 2,310 x 13 plus one you get 30,031 which is not a prime. I thought, by what I was reading, that by mulitplying all the primes together you would always get a number that if added to one would be a higher prime. I guess there is no such formula.
AxiomOfChoice
AxiomOfChoice
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December 16th, 2013 at 3:52:13 PM permalink
Quote: Greasyjohn

Thanks everyone for your replies. I have the book One Two Three Infinity and just love this stuff. I had thought that what was being stated ( which I didn't grasp) was that if you multiply primes ie, 2x3x5x7x11x13 etc., that the answer you get after any multiplication (plus one) is a prime. But when you get to 2,310 x 13 plus one you get 30,031 which is not a prime. I thought, by what I was reading, that by mulitplying all the primes together you would always get a number that if added to one would be a higher prime. I guess there is no such formula.



Don't feel bad about it. I thought this too the first time I saw this proof (it was near the beginning of my math education). It takes a while to get used to mathematical rigor!
Mosca
Mosca
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December 16th, 2013 at 4:55:30 PM permalink
Prime numbers have driven people mad, just so you know. You want to have some fun? How about twin primes. 11 and 13, 17 and 19. So you're rockin' along, and you're thinking, "Man, the higher I get, the less common these things are. 41 and 43, 59 and 61, 71 and 73..."

Guess what: it is conjectured that there are infinite twin primes. Currently the highest known twin primes are 2003663613 · 2^195000 ± 1.

This is an area where patterns and beauty are tantalizingly close, but the best pure mathematicians who ever lived have not been able to pin down formulas that describe their behavior.
NO KILL I
thecesspit
thecesspit
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December 16th, 2013 at 6:13:04 PM permalink
Quote: Greasyjohn

Thanks everyone for your replies. I have the book One Two Three Infinity and just love this stuff. I had thought that what was being stated ( which I didn't grasp) was that if you multiply primes ie, 2x3x5x7x11x13 etc., that the answer you get after any multiplication (plus one) is a prime. But when you get to 2,310 x 13 plus one you get 30,031 which is not a prime. I thought, by what I was reading, that by mulitplying all the primes together you would always get a number that if added to one would be a higher prime. I guess there is no such formula.



30,031 is prime though.

Your thought was correct. Multiple all the primes below any number together, add one, you'll have a prime number. Just pick a number, find all the primes, and away you go.

This method doesn't calculate all the primes, though. Just shows that there is always a higher one.

EDIT : this post is incorrect.
"Then you can admire the real gambler, who has neither eaten, slept, thought nor lived, he has so smarted under the scourge of his martingale, so suffered on the rack of his desire for a coup at trente-et-quarante" - Honore de Balzac, 1829
AxiomOfChoice
AxiomOfChoice
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December 16th, 2013 at 6:17:01 PM permalink
Quote: thecesspit

Your thought was correct. Multiple all the primes below any number together, add one, you'll have a prime number.



That's not correct.
AxiomOfChoice
AxiomOfChoice
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December 16th, 2013 at 6:18:39 PM permalink
In fact, what do you think 59 * 509 is?
thecesspit
thecesspit
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December 16th, 2013 at 6:58:11 PM permalink
Quote: AxiomOfChoice

In fact, what do you think 59 * 509 is?



Derp... Apologies. 30,031... I totally misunderstood the point of the proof, and will now go shut the hell up :D
"Then you can admire the real gambler, who has neither eaten, slept, thought nor lived, he has so smarted under the scourge of his martingale, so suffered on the rack of his desire for a coup at trente-et-quarante" - Honore de Balzac, 1829
AxiomOfChoice
AxiomOfChoice
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December 16th, 2013 at 7:03:28 PM permalink
Quote: thecesspit

Derp... Apologies. 30,031... I totally misunderstood the point of the proof, and will now go shut the hell up :D



Heh, no problem. As I said, I made the exact same mistake the first time I heard the proof. It's kind of subtle!

The key is that, even though the product + 1 can't be divided by any primes in your original list, there might be primes higher than the numbers in the list but still lower than the product + 1. So it could be divisible by "medium-sized" primes only. (This still violates the assumption that the list is complete, of course, so the proof still holds)
s2dbaker
s2dbaker
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December 16th, 2013 at 8:36:07 PM permalink
Quote: Greasyjohn

Thanks everyone for your responses. I'm still in the dark. An example of the equation might help. 2x 3 x 5 x7 plus one is a prime, 211, but if you continue with the calculation and multiply 210 x 9 plus 1 you get 1,891 which is not a prime. If someone could write out the calculation that when added to 1 is always a prime, that would be great!

9 is not prime.
Someday, joor goin' to see the name of Googie Gomez in lights and joor goin' to say to joorself, "Was that her?" and then joor goin' to answer to joorself, "That was her!" But you know somethin' mister? I was always her yuss nobody knows it! - Googie Gomez
s2dbaker
s2dbaker
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December 16th, 2013 at 9:03:22 PM permalink
Quote: AxiomOfChoice

In general, finding large primes is computationally difficult! There is no easy way to generate them.

I used to do Mersenne Primes but my CPU kept heating up and crashing the calc. I would only be successful about 80% of the time with each iteration taking a month. It sucks to lose nearly a month's worth a work because your CPU fan is too small or not perfectly seated. Now I play Bejeweled Blitz and my CPU is much happier.
Someday, joor goin' to see the name of Googie Gomez in lights and joor goin' to say to joorself, "Was that her?" and then joor goin' to answer to joorself, "That was her!" But you know somethin' mister? I was always her yuss nobody knows it! - Googie Gomez

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