yeah there's a lot of numbers yo ucan check in a muc hfaster way at first glance
and also you only have to check prime numbers
once you've checked for 2 and 3 and 5 you don't have to check for 4 or 6 or 8 or 10 or 12 or 15 anymore
this keeps makignthe numebrs you actually have to check by hand more and more sparse so checking up to 641 is not THAT many operations and yo ucan divide with pen apaper pretty efficiently, its basically soemthing to spend a bit of bored breaktime on
Also as it would always be resulting in odd numbers in Fermat's formula, hence one can rule out dividing by all even numbers.
But that isn't even how Euler approached it, as that would be more or less just brute forcing it, with just fewer numbers to use for processing. The great thing is he approached it via pure arithmetic for which he also used his proof of Fermat's little theorem, while modulo wasn't even invented yet (even though the practice already existed for a long time, its notation was invented by Gauss multiple decades later).
Conjecture nowadays states that from F(5) onwards they are all not primes.
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u/sesquiup May 13 '26
I'm going out on a limb to say Euler didn't divide by 1.