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Re: Newly Discovered Titanic Prime
Posted:
Oct 8, 2001 11:45 AM
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Denis Feldmann wrote:
> > That number is not prime.
>
> Why are you so confident?
>
> >
> > I used ProvablePrimeQ on the number and it returned False.
>
> Maple answers isprime (10*((10^1139-1)/9)+9+9*10^1140) by "true" after 1 mn
> 30 on my PC. Admittedly, this is only probabilistic testing, but no
> counterexample has ever been found for isprime
> (from the Maple "help" file :
> "The function isprime is a probabilistic primality testing routine.
> It returns false if n is shown to be composite within one strong
> pseudo-primality test and one Lucas test and returns true otherwise. If
> isprime returns true, n is ``very probably'' prime - see Knuth ``The art of
> computer programming'', Vol 2, 2nd edition, Section 4.5.4, Algorithm P for a
> reference and H. Reisel, ``Prime numbers and computer methods for
> factorization''. No counter example is known and it has been conjectured
> that such a counter example must be hundreds of digits long." )
Download Marcel Martin's 'Primo' to prove the number using ECPP. It
should take only an hour or so, as it's a small number.
http://primepages.org/ has a links section which will point to it, or a
google search for it. It is the current ECPP world record holder, and
runs on most x86 windows platforms, and also under Wine on x86
Linux/*BSD.
Phil
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