Subject: Re: 7*10^9543+1 is Prime?
From: Paul Landon <[email-masked]>
To: [email-masked]
Date: Wed, 09 Aug 2000 18:15:51 +0200

Strange!
We'd best let Chris Nash answer that one!

Cheers,
Paul Landon

Milton Brown wrote:

> PrimeForm on another computer, copy of its certificate
> below
>
> :N-1
> :composite
> // 7*10^9543+1
> // N=FR+1, F=
> :F
> _18D62DEE_
> // X=1187^((N-1)/5)=
> _8A9B0544_
> // gcd(X-1,N)=1
> // X^5=
> _78C2F375_
>
> Paul Landon wrote:
>
> > Hiya Milton,
> >
> > what said it was composite?
> >
> > Cheers,
> > Paul
> >
> > Milton Brown wrote:
> >
> > > Hi all,
> > >
> > > One of my computers says, on PrimeForm,
> > >
> > >       7*10^9543+1  is prime!
> > >
> > >       [N-1, Brillhart-Lehmer-Selfridge][digits: 9544]
> > >
> > > copy of certificate below. The other computer,
> > > did not provide this analysis, but said it was composite.
> > >
> > > What is it?
> > >
> > > Milton L. Brown
> > > [email-masked]
> > >
> > > :N-1
> > > :prime
> > > // 7*10^9543+1
> > > // N=FR+1, F=
> > > :F
> > > _18D62DEE_
> > > // X=13^((N-1)/5)=
> > > _33E816AE_
> > > // gcd(X-1,N)=1
> > > // X^5=1
> > > // Conclusion: All factors of N are =1 mod F (Pocklington)
> > > // Assume N=(Fa+1)(Fb+1), a,b>=1
> > > // Write R=FP+Q
> > > // P=
> > > _00000000_
> > > // Q=
> > > _9BE5BB13_
> > > // To solve: ab=(P-k), a+b=kF+Q, test (kF+Q)^2-4(P-k)
> > > // is a square
> > > // No solutions for k>=0