Can you help me to prove that for every prime number p, sequence 1+p, 1+2p, 1+3p,... has an infinite number of prime numbers. (and same thing for every positive integer n, that sequence 1+n, 1+2n, 1+3n,... has an infinite number of prime numbers).
Can you help me to prove that for every prime number p, sequence 1+p, 1+2p, 1+3p,... has an infinite number of prime numbers. (and same thing for every positive integer n, that sequence 1+n, 1+2n, 1+3n,... has an infinite number of prime numbers).
No, I can't help you. These are both particular instances of Dirichlet's Theorem - https://en.wikipedia.org/wiki/Dirich...c_progressions. This is an advanced theorem in number theory with no known simple proof.