Largest Twin Prime Yet Discovered

Chris Chiasson writes "The Twin Internet Prime Search and PrimeGrid have recently discovered the largest known twin prime. A twin prime is a pair of prime numbers separated by the integer two. The pair discovered on January 15th was 2003663613 * 2^195,000 ± 1. The two primes are 58,711 digits long. The discoverer was Eric Vautier, from France."

Good example of a /. story.

[Ninjaesque One]

Succinct, on a subject undeniably nerdy, and mostly devoid of spelling mistakes. Also, not 'edited' by Zonk.

Re:Are you kidding?

[fredmosby]

How about 2 and 5.

Re:Don't seem too excited

[cgibbard]

Finding twin primes like this is mostly just an elaborate computational game which doesn't really tell much about the mathematical structure of twin primes. It doesn't help at all with knowing whether there are infinitely many or not, for example. The same goes for other searches for large primes.

Also, if you're asking about real-world practical considerations, the primes used in practical work by comparison are tiny. Using such large primes for things like cryptography would be stupid for a number of reasons, not the least of which being that there are only so many known such primes out there, the size of your key would give it away. Personally, I don't know of any practical use for twin-primes or Mersenne primes, or any of the other classes of large primes being searched for.

It's really more just for fun, like computing digits of pi. However, devising new ways to access large twin primes, for instance, results in improvements of our knowledge of them. It's those new theorems and algorithms which people might get excited about. Running a computer for hours or days or months to actually find the things is less interesting. ;)

Re:Are you kidding?

[Anonymous Coward]

Mathematicians have been known to alter the primality of 1 based on convenience. Generally it doesn't matter very much whether you consider it prime or not.

NO NO NO

[Kjella]

Well then (P(1)*P(2)*...*P(n))+1 must be prime:

No, no and even more no. Let's say my list of known primes is (3,5). 3*5+1 = 16 is not prime, all you've proven is that your list of primes is incomplete. It is only an existance theorem, and can not be used to find new primes.

Re:NO NO NO

[Kjella]

Reread your formulation once again, and you claim you can list all primes less than p(n), which is different than the standard formulation of Euclid (he just says, take a list of known primes). But you're still wrong:

2*3*5*7*11*13=30030
30030+1=59*509

yes yes yes yes

[wpegden]

The poster is not wrong, his proof is correct. It is a proof by contradiction. He ASSUMES (for the sake of trying to find a contradiction), that there are finitely many primes P(1), ..., P(n). If there WERE only those finitely many primes, than the number P(1)*...*P(n)+1 WOULD be prime (because it's not divisible by any of them), which WOULD be a contradiction. Get it? Of course it's true that 2*3*5*7*11*13+1 may not be prime. But the poster didn't prove that P(1)*...*P(n)+1 is ALWAYS prime, he proved it was prime IF those are the only primes, which is enough to get a contradiction.

Anyways, talking about what Euclid did is kind of irrelevant here (except from a historical perspective, of course). What he said wouldn't hold up in most math classes these days. Rather than doing an actual general proof, he says, "assume there are only 3 primes p,q,r. Then p*q*r+1 would also be prime, contradiction!" or something like that. Proof conventions have changed somewhat since then ;)

Anyways, I guess this shows us that Slashdot's moderation system is no substitute for peer review in mathematics, even for really basic problems... surprise!