Quote:
Originally Posted by JeppeSN
I was creating a new OEIS entry as a kind of procrastination...
I wonder what the first (probable) prime of the form \(a^{16384}+b^{16384}\) is. Since this type of (extended) generalized Fermat numbers is mentioned in many sources (in the web), I would think someone had determined the answer? I had no lucky googling.
For each \(m<14\), brute force will relatively early find a probable prime \(a^{2^m}+b^{2^m}\). The last of these is \(72^{8192} + 43^{8192}\) which can be found i Caldwell's database: 72^8192 + 43^8192
So what about \(m \ge 14\)?
/JeppeSN

a and b must be coprime. Their powers can't be addiive inverse remainders of each other.Etc.