Hi, Dirichlet's theorem states that any arithmetic progression a+kb, where k is a natural number and a and b are relatively prime, contains infinite number of primes. I'm wondering if there is an easy proof of a much weaker statement: every arithmetic progression a+kb where gcd(a,b)=1 contains at least one prime. I can't come up with a satisfactory proof, but I have a feeling it shouldn't be too hard. Does anyone have any ideas? Thanks.