SP9587 PRIMEZUK - The Prime conjecture

Euclid may have been the first to prove that there are infinitely many primes. Let's walk through his proof, as even today, it's regarded as an excellent model of reasoning. Let us assume the converse, that there only a finite number of primes: p $ _{1} $ , p $ _{2} $ , ..., p $ _{n} $ . Let **m** = 1 + $ _{i=1} $ Π $ ^{n } $ p $ _{i,} $ i.e. the product of all of these primes plus one. Since this number is bigger than any of the primes on our list, m must be composite. Therefore, some prime must divide it. But which prime? In fact, m leaves a reminder of 1 when divided by any prime p $ _{i} $ , for 1

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