Sieving Question
 

What advanced knowledge do we have about the factors of the following numbers?

P = (k*2^m)^(2^n)+1

where k is an odd 32-bit number, and m ~ n.

The idea is to use Proth's theorem for a primality check and do convolutions using Schoenhage-Strassen with carries in base-(k*2^m).

Factors will be = s*2[SUP]n+1[/SUP]+1.