Re: [PrimeNumbers] GFPS
> There are some questions about GF(n,b).The test was not implemented in GFNSieve or in Proth.
> 1) Why GFNSieve doesn't remove b's which are odd
> powers of even numbers (e.g., 216)?
> Why doesn't Proth immediately report them composite?
I considered that the proportion of GFN, with b's which are odd powers,
and which have no small factor, is so small that this optimization was
> 2) Do all GFPS contributors take this into account?I think that none takes this into account.
> 3) Do all GFPS contributors take into account that theNo. The small b's are double-checked because of your remark and I think that
> most of b's which are perfect squares are already tested
> (with smaller n), and enough small b's may also be
> already tested (with bigger n)?
it's a good point. In a first step, the numbers are tested with small b (for
example 262144 and b < 1000). When 131072 is completed, this range will be
double checked. But the proportion of numbers that will be tested twice is