From: Spike Jones (spike66@ibm.net)
Date: Wed May 10 2000 - 22:08:54 MDT
> Michael M. Butler wrote:
>
> > Gee Whillikers, Spike, you use kitchen arithmetic better'n... well, I
> > can't say that, on account of the little'uns....
Spike wrote:
> Wow thanks, Mike. With that introduction, I will mention that
> we do in fact have an extropians GIMPS team, sort of. Recall
> from a few months ago that GIMPS is an organized effort to
> search for enormous prime numbers, and Mersenne primes are a
> special class of primes, of the form 2^n-1, such that they have
> a shortcut to determining their primeness. This shortcut allows
> the determination of primeness to be dozens of orders of magnitude
> faster than ordinary factoring. [Now theres a phrase one seldom
> hears: dozens of orders of magnitude.]
Dooooooh! I cant believe I made such a comical error. In order
to prove the primeness of the largest known prime number
[as of 1 June 1999] would require on the order of 10^1,000,000
divides, since the largest known prime number has well over 2 million
decimal digits. Then it matters not if one uses Newtons method
or any of the sieves, or any other shortcut, for these might at
best knock off a few or maybe even a few dozen orders of magnitude,
but what matter is that, when we speak of 10^1,000,000? So
the Lucal Lehmer shortcut for determining primeness of a
Mersenne prime is shorter than factoring by over a million
orders of magnitude. And it matters not if that Lucas Lehmer
takes a nanosecond, a year or a lifetime, these all being within
what, 20 orders of magnitude of the same? The ratio is *still*
way over a million orders of magnitude.
On a sobering note, it was Sasha Chislenko who got around to
actually setting up the extropians GIMPS team. I tried to do it
about a year ago but evidently did something wrong. I noticed
in the GIMPS archives that it was Sasha that actually managed
to make it happen. If you want to join the extropians GIMPS
team, Go to the site and follow the directions.
If I can figure out what I was doing wrong before,
I intend to donate my 6 processor years of Mersenne prime
searching to the extropian GIMPS team in honor of the memory
of Sasha, the mathematician.
spike
http://www.mersenne.org/prime.htm
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