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Old 2018-03-15, 10:37   #2
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"Forget I exist"
Jul 2009

8,369 Posts

Originally Posted by JeppeSN View Post
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 \(m \ge 14\)?

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