Please excuse the ignorance, but something puzzles me.

If a sieving run finds a factor in PSP, than that particular number is composite, correct? Therefore the k associated with that number is a Prime Siersinski number. Since we are searching for "ks" lower than the lowest known, haven't we just found a new lowest? What am I missing?

Thanks,
Jim

A Sierpinski number is a k for which k*2^n+1 is composite for EVERY n. We are just showing one n at a time that k*2^n+1 is composite.

We can NOT show that a k value IS a Sierpinski number this way, all we can do is look for an n value for which k*2^n+1 is PRIME. If we find a single n value that makes k*2^n+1 prime, then we have shown that k is NOT a Sierpinski number.

Hope that helps.
CW

I was missing the "EVERY".

Thanks,
Jim