# Large Mersenne primes

1. Dec 18, 2009

### Pagan Harpoon

http://mathworld.wolfram.com/news/2009-06-07/mersenne-47/

When a new large number such as this is discovered, does anything interesting usually follow from it or does everyone say "Yes... there it is, now let's find the next one."?

2. Dec 19, 2009

### CRGreathouse

Pretty much that.

There's some interest in looking at the distribution of primes, but there's only so much you can deduce from one more prime.

3. Dec 19, 2009

### robert Ihnot

Pretty much that. CRGreathouse

The problem begins with Euclid and the study of perfect numbers. It was brought into the 17th Century by Mersenne, who made some guesses, which interested others. Euler in 1772 proved the primality of 2^31-1.

There are some fairly simple criterion for primes that might be divisors, for example: A prime divisor of 2^p-1 must be of the form 2mp+1. 2^11 being such a composite case having both 23 and 89 as divisors. Also p is of the form 8k plus or minus 1 (which means that 2 is a quadratic residue modulo p). Of course if 2^q-1 is prime then so is q.

So it seems interest is mostly because of the historical value, the ease with which many potential factors are eliminated, and the vast size of the potential prime. Most of the very large primes discovered are Mersenne.

Last edited: Dec 19, 2009
4. Dec 19, 2009

### Pagan Harpoon

Thank you for clarifying.