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Originally posted by ipsedixit
I think two is a pseudo, or accidental prime, a chameleon which takes on the appearance of being a prime by the accident of it's proximity to one. I don't think it belongs in the pattern of the primes at all.
I wonder if all the trouble mathematicians are having in discovering the pattern of the primes is, in some way, related to a mistaken assumption of the presence in that pattern of the number two.
Is two a pseudo prime?
Originally posted by stander
Whether Two should or should not belong to the population of prime numbers is decided on a completetely different criterion than it's even/odd membership.
The FTA basically says that every integer greater than 1 is a unique product of primes.
Originally posted by ipsedixit
Perhaps I am wrong in this, but I thought that the only criterion for considering a number a prime is that it be evenly divisible uniquely by one and itself.
But besides that, prime numbers have nothing to do with addition ...
tauristercus, why don't you include numbers 2 and 3 as primes in your first diagram? I read that far and came to a screeching halt.
Originally posted by zerotensor
Here is a graphic representation the first 500 prime numbers in binary.
I generated the picture with a couple lines of code in Mathematica.
Originally posted by nablator
There is nothing unique about 2 or 3. Except that they are the smallest two primes. "No other prime is even" means the same as "no other prime (than 2) is a multiple of 2". But you can also say that no other prime than 17 is a multiple of 17. Nothing special.