From: Spike Jones (spike66@ibm.net)
Date: Wed Aug 11 1999 - 00:03:23 MDT
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
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
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