[QUOTE=fivemack;378883]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.[/QUOTE]

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

[QUOTE=fivemack;378883]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.[/QUOTE]

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

[QUOTE=R.D. Silverman;378873]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:

[b]CONJECTURED[/b] 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.[/QUOTE]

[URL="https://docs.google.com/viewer?a=v&pid=sites&srcid=ZGVmYXVsdGRvbWFpbnxwZWRqYXByaW11c3xneDoyN2Q1OGI1N2ZhMGY5MWZj"]Conjectured Polynomial Time Primality Tests for Numbers of Special Forms[/URL]