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Comment by lanna | Hacker News Reader

Why do you think 2 is alien? How could the fundamental theorem of arithmetic be stated without 2?

2 isn’t an alien, exactly... but it’s a little bit of an oddball amongst the primes. There are indeed a lot of theorems that start with “let p be an odd prime.”

2 is definitely no “alien”. More like a legendary prime god amongst countably infinite odd primes. 0 and 1 are two sides of an extreme that either generates a meaningful number system through their separation and extremis from one another or no system at all if 1=0 is assumed true. They’re like a Jekyl and Hyde god.

"Odd" is just a word that means "not divisible by two". There is truly nothing special about a prime not being divisible by two. I could equally say "3 is a legendary prime god amongst countably infinite non-divisible-by-three primes", "5 is a legendary prime god amongst countably infinite non-divisible-by-five primes"... The only difference is that we do not have special words that mean non-divisible-by-three, non-divisible-by-five, etc.

In this regard, I don't see 2 as a special prime. Saying "2 is the only even prime" is the same as saying "2 is the only prime divisible by two", which, by definition, can be said about any other prime.

Right. In the language of the article, if p is a whole number whose digits end in the number 2 then all numbers after it ending in the digits 0 or 2 are not prime. It’s a seemingly weak statement but it says a much stronger thing about the primes than the hypothesis of the article.

Anyway, just trying to react in tone to calling any number an “alien”. I think of numbers as being outside the realm of words like alien - I don’t even know what that would mean for a number. Hence my comment is hyperbole hinting at my love of mathematics. To me, it really is a beautiful area of study. Wish I could do it more.

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