GIMPS team

Spike Jones (spike66@ibm.net)
Tue, 10 Aug 1999 23:03:23 -0700

We are trying to discover the next Mersenne prime, a mersenne prime being a prime of the form 2^n-1, where n is prime. (If n is composite, then 2^n-1 must be composite.)

There are 38 known Mersenne primes. The reason these are special is that there is a shortcut known as the Lucas Lehmer test which speeds the time to determine primeness by a factor of, well... If a typical 2 million digit number is tested via LL by a typical modern desktop computer, it takes about 5 weeks, whereas the same number tested by trial factoring (which is how a non-mersenne would need to be tested) would take longer than the time until heat death of the universe, even if every computer ever manufactured were to be dedicated exclusively to that task.

Consequently, the latest Mersenne prime is also the largest known prime, and also, the discoverer knows from that prime the largest known perfect number (which is a number that equals the sum of its factors, such as 6 and 28) since (2^n-1)*(2^(n-1)) is a perfect number if 2^n-1 is prime. Example, n=5, 2^n-1=31, 31*16=496 which is the sum of its factors.

As a side benefit, the LL algorithm provides a free system diagnostic, since a bit error will show up as a wacky intermediate result. One of my confusers, I mean computers, started getting bit errors a week before the power supply failed. The GIMPS algorithm will also show up a defective processor, or an overclocked counterfeit processor, etc.

Any other takers? spike