View Single Post
2018-03-15, 10:37   #2
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

8,369 Posts

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.