Do prime numbers follow a certain mathematical system like odd and even numbers for exmple?

Question

Do prime numbers follow a certain mathematical system like odd and even numbers for exmple?

Answer 1

"Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers, and we have reason to believe that it is a mystery into which the human mind will never penetrate." — Leonhard Euler



We don't know if there is a pattern, but if it is, it's pretty complicated. The formula x^2 + x + 41 gives primes up to 40, but that's as far as it'll go.



There is a possible pattern with the distribution of primes, but this has not been proven, and if you manage to prove the Reimann hypothesis, you'll be plenty rich!

Answer 2

Well, this is certainly more complicated than I thought. There's no simple polynomial (like A*X^2 + B*X + C) of any order (i.e., you can start with X^N for N as large as you like) that will always result in a prime number.



However, there are complicated multi-variable polynomials which will generate primes. See the link to MathWorld below.

Answer 3

no i dont think so