Prime numbers—integers that are divisible only by themselves and 1—are the easiest path into understanding both rigor and mysticism in mathematics. Euclid’s proof that there is an infinite number of prime numbers is both one of the simplest mathematical proofs and one of the oldest. Late last month, Curtis Cooper of the University of Central Missouri moved one small step closer to Euclid’s infinity, when he announced that 2^{57,885,161}-1 is prime. This is now the largest known prime number, eclipsing the previous record-holder, which had been discovered at UCLA in 2008. The new number has 17,425,170 digits—just writing them down makes for a 22.45-megabyte text file. The UCLA number had knocked an earlier number of Cooper’s, from 2006, out of the record books. With apologies to the Magnetic Fields, the book of primes is long and boring, but an addition to that book is a good chance to look for the music within it.

Cooper and a group at UCLA have been swapping records as part of a common effort called GIMPS, the Great Internet Mersenne Prime Search. Mersenne primes are numbers like 3=2^{2}-1 , 7=2^{3}-1 or 31=2^{5}-1 that are 1 less than a power

Source: Future Tense Articles