[Axiom-developer] Re: factor bug

[William Sit]

On Mon, 18 Dec 2006 05:00:12 -0500
 root <address@hidden> wrote:
> NAG                      MAY18/05                DEC14/06
> f:=119646463             f:=119646463 
>           f:=119646463
> factor f => 119646463    factor f => 119646463   factor f 
> => 119646463
> prime? f => false        prime? f => false       prime? f 
> => false
> g:=129864979             g:=129864979 
>           g:=129864979
> factor g => 11027 11777  factor g => 129864979   factor g 
> => 129864979
> prime? g => false        prime? g => false       prime? g 
> => false
> g-11027*11777 => 0       g-11027*11777 => 0 
>     g-11027*11777 => 0
>
> m:=119643463             m:=119643463 
>           m:=119643463
> factor m => 119643463    factor m => 119643463   factor m 
> => 119643463
> prime? m => false        prime? m => false       prime? m 
> => false
> m - 10111*11833 => 0     m - 10111*11833 => 0    m - 
> 10111*11833 => 0
>
> Clearly we've found a counter-example to one of the 
> fundamental
> theorems of number theory. :-)
>
> Tim

So you confirmed that even the NAG version exhibited 
problems? Just hope no one uses these two "primes" for 
RSA.

William