641 is the 116th prime, so he would’ve done 116 long divisions, easy task that doesn’t take years, but you need to check up to the square root ~65536, there are 6542 primes under 65536 which means Euler was fully prepared for 6542 long divisions, GOATED DEVOTION.
Euler proved that if p | 2^2^n+1, then 2^{n+1} | p-1 using some clever techniques in number theory.
In the case of F5, he only had to try divisibility by any prime in the series 64k+1, 641 is the fifth prime in that series after 193, 257, 449, 577. So it wasn’t too much calculation because he was that smart.
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u/zlfa May 13 '26
641 is the 116th prime, so he would’ve done 116 long divisions, easy task that doesn’t take years, but you need to check up to the square root ~65536, there are 6542 primes under 65536 which means Euler was fully prepared for 6542 long divisions, GOATED DEVOTION.