The only known Primes of this form are 3, 5, 17, 257, and 65537.

I note that these are all primes of the form 2^n+1, where n is a power of two.


Are these the Mersenne Primes? Something like (2^(2^n))+1? I think I remember something about the series failing at n>3, with the counterexample for n=4 being publically and painstakingly rendered on the blackboard in front of the assembled multitudes, one of the factors being 671...Does that sound familiar to anyone? But I don't recall ever coming across the numbers in the context of constructing regular polygons.