====== Prime Numbers ======

Since all other whole numbers (except 0) can be produced by multiplying together [[http://en.wikipedia.org/wiki/Primes|primes]] – they must be considered fundamental.

(1), 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31 &etc

There are an infinite number of primes - as proved by Euclid around 300B.C. ( [[https://en.wikipedia.org/wiki/Euclid%27s_theorem#Euclid's_proof|Ref.]] ). Although billions of them have so far been found (nowadays via computational 'sieving' algorithms), they appear to be randomly distributed - but with some 'rules' - for example, they become more rare as the numbers get bigger. As yet there’s no proven mathematical method which can accurately predict where the next one will be.

//Note:// As at Oct. 2024. the largest known prime number (discovered via collaborative networked computer processing) has 41,024,320 digits ([[https://www.mersenne.org/primes/?press=M136279841|ref.]])

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Also see: [[content:mathematics:riemann_hypothesis|The Riemann hypothesis]] and [[content:mathematics:legendre_conjecture]] and [[content:mathematics:oppermann_conjecture]]

Note: The true nature of [[content:mathematics:random_numbers|randomness]] itself is also under discussion.

~~stars>4/5~~