alarming inefficiency ( modular arithmetic )

[Igor Schein <igor@txc.com>]

Hi,

from a posting on sci.math:

p = 2^29440 - 2^27392 + 1
b = 2^32
k = (p-1)/2^10

I did Mod(b,p)^k in gp

it took 20 min on Linux 450MHz PC.

However, from a follow-up to the same posting, Magma only takes
8 min ( not clear on what platform, but I'm certain it's as fast
or slower than my machine ).

So, I am wondering, if there's still room for improvement, because
I believe Pari should be able to beat Magma in speed.

Thanks

Igor