On Tue, May 6, 2008 at 10:15 AM,  <[EMAIL PROTECTED]> wrote:
>
>  William has mentioned some congruence tests that we can perform -- I'd like 
> to make sure that I got the right answer before we pat ourselves on the back 
> too much.
>
>

David Harvey's congruence tests would be pretty good.  Just choose
*any* prime p > 10^7 + 10
say and compute B_{10^7+4} modulo it using David Harvey's function;

sage: p = next_prime(10^7+10)
sage: time bernoulli_mod_p_single(p, 10^7+4)
CPU times: user 0.49 s, sys: 0.00 s, total: 0.49 s
Wall time: 0.51
8087583

Pretty cool, eh?

William

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