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Using way simpler math, the probability that an even number is prime is zero. One cannot conclude from that that there are no even primes (in fact, many mathematicians think the smallest prime is even (https://cs.uwaterloo.ca/journals/JIS/VOL15/Caldwell2/cald6.h... ))

Mathematicians do use this kind of back of the envelope calculations to get a feeling for whether a statement may be true, but they can never prove something.

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I don't quite understand your comment.

First, the smallest prime (2) is even.

Second, your first statement can substitute "an even number is prime" with "a multiple of n is prime" for all prime n, leading us to conclude that the odds of any multiple of 3, 5, 7, 11, 13, et al being prime are zero thus seemingly statistically disproving the existence of any prime number which is absurd.

> in fact, many mathematicians think the smallest prime is even

Up to sign? The smallest prime is even.

1 could be a prime, too, as for example Legendre, Lesbegue, Cayley (in the Encyclopædia Britannica), Kronecker, Hardy and Sagan stated at least once (see the URL I linked to earlier)

One isn't typically called a prime for the same reason as mathematicians typically say 0^0 equals 1; it makes many theorems and proofs look better.

Hm. I'm a mathematician. I always thought it wasn't called prime because it breaks uniqueness for the fundamental theorem of arithmetic.

It makes it look pret29th!

Your link doesn't work for me…

Remove trailing ):

https://cs.uwaterloo.ca/journals/JIS/VOL15/Caldwell2/cald6.h...

HN's URL detector doesn't handle nested parentheses, it seems. I added a space to fix this.

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