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.

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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.

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a small driver

sample output