# Re: GIMPS team

Brian Atkins (brian@posthuman.com)
Wed, 11 Aug 1999 03:38:09 -0400

I'm considering defecting from SETI, but not yet. I got 7 CPUs currently.

Spike Jones wrote:
>
> Looks like the extropian GIMPS team is a go. A generous
> benefactor has unveiled a mac farm.
>
> 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
>
> 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

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