How to prove that there are infinitely many primes It's urgent

Counter proof: suppose that there are only n primes P1, P2,..., PN. Then multiply these n primes and add 1 to get p1p2... PN + 1. It's easy to find that this number is divided by P1, P2, and PN, so this number can't be divided by any one of P1, P2,..., PN, so this number is a prime different from P1, P2,..., PN, which is contradictory to the assumption. So there are infinitely many primes

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