>>>Yup. And don't forget that the larger the exponent, the fewer the
>>>possible factors in a given range (e.g., from 0 to 2^40 or 0 to 2^63).
>>>
>>
>>Ok, I'll ask the stupid question, I stopped maths at the year before
>>university, WHY is this the case?
> Because a factor of Mp must be of the form 2*k*p+1 (actually only half of
> those are possible), and as p increases the number of potential factors of th
> at form <= X decreases.
Actually, it 2*k*p+1 must be ==+/-1 mod 8 which is 2/8=1/4. This can be
further reduced by checking for divisibility by 3, and 5.
So thats 1/(15*p) of numbers that we are actually checking.
-Lucas Wiman
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