This problem seems to be fixed in pari-2.4.2
(not yet realead!, code in CVS)

?numbpart((5*10535+4))
time = 16 ms.
%2 = 
13277569485341661441070935908285030462857350709714871167223602317834599507871542657403046634712636713000828040255875556477097762416076415269139010200121379629789951459033537585723875697364877024644629549129563676618917774238138926865673007168971398575

The CHANGES file says:

Fixed
"12- numbpart inaccurate (and slow). E.g numbpart(52602) off by 1 [#557]."

This version of pari also includes some new functions that could be
useful to Sage.

For example, it includes the function polhermite and  pollegendre, for
computing the
Hermite and Lengendre orthogonal polynomials, that currently sage
computes using maxima
and I think that using libpari could be much faster.

Pablo




On 7/26/07, Bill Hart <[EMAIL PROTECTED]> wrote:
>
> Pari implements it, but incorrectly:
>
> sage: number_of_partitions(5*10535+4,algorithm="pari")
> 132775694853416614410709359082850304628573507097
> 148711672236023178345995078715426574030466347126
> 367130008280402558755564770977624160764152691390
> 102001213796297899514590335375857238756973648770
> 246446295491295636766189177742381389268656730071
> 68971398574
>
> But:
>
> sage: number_of_partitions(5*10535+4)
> 132775694853416614410709359082850304628573507097
> 148711672236023178345995078715426574030466347126
> 367130008280402558755564770977624160764152691390
> 102001213796297899514590335375857238756973648770
> 246446295491295636766189177742381389268656730071
> 68971398575
>

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