catalogue

so this is a simple proof on the infinitude of primes that im paraphrasing from euclid. well i guess its more of a paraphrase of a paraphrase since the direct translation uses lengths and such (greeks were heavy on the concrete). ANYWAY

Say there is a finite list of prime numbers, and say there are n of them. Now we multiply all these primes P1P2P3P3P5…Pn. Call this product of all known primes φ. now lets add 1 so we have φ+1. if we divide this number by any of the known primes were always going to have a remainder of at least 1 (since we added the one to the product of all the primes) therefore either this new number φ+1 is a prime or there is some prime that we didnt list before. since you can do this for any number of primes there is an infinite number of primes. voila!