> There are some questions about GF(n,b).

> 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?

The test was not implemented in GFNSieve or in Proth.

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

not needed.

> 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 the

> 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)?

No. The small b's are double-checked because of your remark and I think that

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

only 1/1000.

Yves