It gets worse: (with GP/PARI 2.4.2):
? default(debug,2)
%5 = 2
? p=nextprime(10^20)
%6 = 100000000000000000039
? isprime(p)
*** isprime: Warning: IFAC: untested integer declared prime.
507526619771207
%7 = 1
-- so one call to isprime(), which supposedly proves a proof, involves
further calls (presumably) to fact() whose reults are not proved.
Another email to pari-dev is in order...
John
On 9/7/07, Bill Hart <[EMAIL PROTECTED]> wrote:
>
> The number field code in Pari relies on factoring the discriminant
> often using MPQS. In particular if you turn debugging mode on, you get
> warnings like this:
>
> *** bnfclassunit: Warning: IFAC: untested integer declared prime.
> 10762727634633706239259776012492757340083
>
> So basically the number field code is no more reliable than a probable
> prime test.
>
> This is bad news if you only want unconditional results from Pari. It
> may not be trivial to get unconditional results from all Pari
> functions.
>
> Bill.
>
>
>
> >
>
--
John Cremona
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