Peter Montgomery wrote:
This gp program verifies the solution and factors n:
n = 63130707451134435989380140059866138830623361447484274774099906755
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
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
From the U.S. mirror site for pari-gp
on June 29, 1999 I reached the url
It led me to this factorization:
This was done by:
WWW Interactive Mathematics Server, Factoris, by XIAO Gang (email:, a tool that factors integers and polynomials.
The program concluded that 130166407115741105132742556824466265630151260716462422214638983 is a prime.