Less GHz days for larger exponents in TF?

[Bdot]

Thanks a lot, I think now I got it ...

[davieddy]

Originally Posted by Mini-Geek

Yes, see http://mersenne.org/various/math.php for the algorithm used to check if a number divides a Mersenne number. It does one step for each bit in the exponent, so the speed for each division would seem to be mainly related to the bit length of the exponent.

Yep. That was my meaning exactly.
A couple of refinements:

1) The first six bits of the exponent generate the number
2^63 at most. If the bits are all 1 we get:
2^1, 2^3 , 2^7, 2^15, 2^31, 2^63, so for testing factors
>2^63, the number of steps in the algorithm is (bits in exponent - 6).

2) The squaring and more importantly the division/modulo steps get
more time consuming with the number of bits in the factor, 64 being
a notable watershed.

David