Java Prime

Here are a few primes

Here is a small program to find primes. It is basically a sieve program. As it finds each prime it eliminates all multiples of that number as possible primes. It will fill your disk with primes.

first thousand primes found by this program
first million primes found by this program

Mersenne primes

The biggest primes known are Mersenne Primes. Mersenne Primes are primes of the form 2^n-1. They are easy to check as they can be found by the Lucas-Lehmer test (see Knuth "Art of Computing v2). Here is a program which checks a number n to see if 2^n-1 is prime. It can be shown that for 2^n-1 to be prime a necessary condition is n is prime. If only we had a list of primes to check.

a small driver
sample output