This gp program verifies the solution and factors n:

n = 63130707451134435989380140059866138830623361447484274774099906755

Mod(2,n)^n

factor(n)

05 Jun 1999 Noam Elkies wrote:

> What is gp?

A free arbitrary-precision arithmetic package with lots of canned data structures (including elliptic curves, p-adic numbers, elements of number fields, etc.) and functions that make it particulary nice for this kind of computation. For instance, to try all n up to 100000 congruent to 1 mod 6:

? forstep(n=1,100000,6,if(lift(mod(2,n)^n-3),,print(n)))

which yields

1

time = 2,650 ms

?

I received this by email June 5, 1999 from a UCLA Mathematics Prof.:

Incidentally, gp is part of pari-gp which is a number theory package developed originally by Henri Cohen and others of Bordeaux, France. It is in wide use by computational number theorists. You can get it from

http://hasse.mathematik.tu-muenchen.de/ntsw/pari/

From the U.S. mirror site for pari-gp

http://www.math.uga.edu/~ntheory/web.html

on June 29, 1999 I reached the url http://www.math.uga.edu/~ntheory/N1.html

It led me to this factorization:

5

97

130166407115741105132742556824466265630151260716462422214638983

This was done by:

http://wims.unice.fr/~wims/wims.cgi?lang=en&module=tool%2Falgebra%2Ffactor.en&cmd=new

WWW Interactive Mathematics Server,

The program concluded that 130166407115741105132742556824466265630151260716462422214638983 is a prime.