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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.

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# Weak form of Dirichlet's theorem

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