New Mersenne prime, for real this time!

GIMPS has just announced today that they have indeed found a new Mersenne prime!

$M32582657 = 2^{32,582,657} - 1$

Obviously I can’t print the whole thing here, but I can tell you that the first 50 digits are 12457502601536945540085550157479950312279598515115, and the last 50 digits are 212445737104635692000092659011752880154053967871. This is now the largest known prime number, breaking the previous record set in December 2005. (Of course there are larger prime numbers — there are infinitely many — but this is the largest number that we can actually point to and say, “this number is prime.”) You can download it here. You can even order a poster of it! (It’s pretty expensive though, since it’s very difficult to print digits tiny enough to make the whole number fit on a poster.)

Unfortunately, at 9,808,358 digits, it’s just shy of the ten million digits needed to claim the \$100,000 prize offered by the EFF. But it’s still pretty exciting.