
Glossary: Prime Pages: Top 5000: 
GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) Mersenne primes have always been the most sought after primes ever since Euclid connected them to perfect numbers over two millennia ago. When searching for new Mersennes, you first look for small divisors (called Mersenne divisors), then apply the LucasLehmer test. These divisors must have a very special form because Fermat and Euler proved: (The proof is linked below.) Sometimes, just the fact that a number divides a Mersenne is enough to show it is prime:
See Also: Mersennes, CunninghamProject Related pages (outside of this work)
Chris K. Caldwell © 19992020 (all rights reserved)
