This k you are testing is a quite heavy one! For k*2^n+/-1, each choice for k has a certain weight, or: the numbers that remain after sieving.

Resieving will not help: sieving is the process to determine which numbers are divisible by a certain numer (in NewPGen, this is 'p'). So all values for 'n' that are divisible by a number 'p', will also be divisible by that same value for 'p' the next time.

As I see it: you (by accident) chose a k that has a very large weight, so non-primes are not easily detected by sieving. I recommend you to stop sieving.

If I am mistaken, please correct me!