Who can help me explain how to prove that there are infinitely many primes Let a = p1p2 × ×pn+1 But a cannot be replaced by P1, P2 So a is a prime, But 2 * 3 * 5 * 7 * 11 * 13 + 1 = 30031 can be divisible. How is this proof right

Who can help me explain how to prove that there are infinitely many primes Let a = p1p2 × ×pn+1 But a cannot be replaced by P1, P2 So a is a prime, But 2 * 3 * 5 * 7 * 11 * 13 + 1 = 30031 can be divisible. How is this proof right

Let's assume that there are finite prime numbers, P1, P2 Except for these, there are no other prime numbers. Your examples are only 2 * 3 * 5 * 7 * 11 * 13. 30031 = 59 * 509 is not included. Many proofs miss this premise. Prime numbers P1, P2... PN make a = p1p2 × X PN + 1A can't be just a prime number, otherwise