What are the Primality Tests ( not factoring! ) for Fermat Numbers?

[R.D. Silverman]

Originally Posted by fivemack

I have a fairly strong suspicion (though I suspect it would need Alan Baker-style techniques to prove it) that no such primes exist; indeed, that no numbers exist for which polcyclo(k,n) is a power of two for k>2, n>0.

Certainly for any given degree for the cyclotomic polynomial
there will be at most finitely many. (via Siegel's Thm)

[CRGreathouse]

Originally Posted by fivemack

I have a fairly strong suspicion (though I suspect it would need Alan Baker-style techniques to prove it) that no such primes exist; indeed, that no numbers exist for which polcyclo(k,n) is a power of two for k>2, n>0.

I think you want n>1, else you have lots of examples.

[primus]

Originally Posted by R.D. Silverman

Your post consists of unnecessary hype. As posted, it makes it appear
as if the content of the paper discusses PROVED results.

It should be titled:

CONJECTURED Primality Criteria for Specific Classes of Proth Numbers


Proth numbers are easy to prove prime anyway because the full factorization
of N-1 follows immediately from the form of the number.

Even if the above conjectures are true, they add very little to the practical art for proving Proth numbers are prime.

Conjectured Polynomial Time Primality Tests for Numbers of Special Forms