Author: Vincent Diepeveen
Date: 08:36:35 05/27/05
Go up one level in this thread
On May 26, 2005 at 17:20:08, Sune Fischer wrote:
>On May 26, 2005 at 16:37:48, Tord Romstad wrote:
>
>>You are right. The largest currently known prime number has 7,816,230 digits.
>>There are now five known prime numbers with more than one million digits.
>
>Why do people keep repeating to me what I said? :)
>
>http://primes.utm.edu/largest.html#biggest
>
>>>Last I checked only a handful or so had been found with more than a million
>>>digits, and of course only through weeks of massively parallel super computer
>>>power.
>>
>>It's not quite that bad. The current record prime was found on a single-CPU
>>P4 2.4 GHz in 50 days. See the GIMPS ("Great Internet Mersenne Prime Search")
>>page for details:
>
>I think these bots just scan a range of mersenne numbers. When they find one
>they can't easily dispute as non-prime it goes through tougher tests for final
>primality verification.
>
>Finding a number that is 99.99% positively prime is "easy", proving it 100% is
>though :)
For real huge primes, finding an industry grade prime is the hard thing.
Proving it to be a prime only means a few mathematicians have got something to
do then.
Especially when the prime is for example p = 5^m * 3^n - 1 or something, you
sometimes have algorithms like needing to prove it's a prime by proving it for
all its factors :
So 3^(p-1) == 3 (mod p)
and 5^(p-1) == 5 (mod p)
if the factors are 3 and 5
Vincent
>-S.
This page took 0.01 seconds to execute
Last modified: Thu, 15 Apr 21 08:11:13 -0700
Current Computer Chess Club Forums at Talkchess. This site by Sean Mintz.