this post was submitted on 09 Aug 2023
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Any examples? Sounds like you mean the reason why one is excluded from the primes because of the fundamental theorem of arithmetic.
No, he's right. "For any odd prime" is a not-unheard-of expression. It is usually to rule out 2 as a trivial case which may need to be handled separately.
https://en.wikipedia.org/wiki/Fermat%27s_theorem_on_sums_of_two_squares
https://www.jstor.org/stable/2047029
https://www.jstor.org/stable/2374361
It's not unheard of no, but if you have to rule out two for some reason it's because of some other arbitrary choice. In the first instance (haven't yet looked at the second and third one) it has to do with the fact that a sum of "two" was chosen arbitrary. You can come up with other things that requires you to exclude primes up to five.
Okay? Like I said, it's usually to rule out cases where 2 is a trivial edge case. It's common enough that "for any odd prime / let p be an odd prime" is a normal expression. That's all.
I just remember it from numberphile, I don't remember what videos sorry.
Wow that was fast I just edited my previous comment and you probably mean "1 and prime numbers" by numberphile with james grime.