It has to be said.
There is just something magical about primes.
I mean they are numbers that represent something basic. Multiplicatively, they can't be broken down and they end up becoming the special cases upon which every mathematical theory must be tried. And yet once you throw them into the world of math theory you get all sorts of weird math facts, that are just undeniably cool.
Like the fact that (p-1)! + 1 is divisible by p, if and only if, p is a prime.
Dude, like awesome.
And yet primes remain mysterious. It was only a few years ago people learned how to test if a number was prime within polynomial time (see here), people still can't prove that there are an infinite number of primes where p and p+2 are prime. And there's the fact that as you go to infinity, the number of primes approaches the function x/ln(x). Zuh?!
I say zuh not because prime numbers are hard to understand, although sometimes they are, but because their wonder and bounty are just mind-boggling.
So let it be understood then, primes are awesome.
And since primes are awesome, math is awesome.
Of course, this is but one of the proofs of math's awesomeness, which are as numerous as prime numbers themselves, and thus proven to be infinite.
6 months ago