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Dirichlet's proof of infinitely many primes in arithmetic progressions waspublished in 1837, introduced L-series for the first time, and it is said tohave started rigorous analytic number theory. Dirichlet uses Euler's earlierwork on the zeta function and the distribution of primes. He first proves asimpler case before going to full generality. The paper was translated fromGerman by R. Stephan and given a reference section.

There are infinitely many prime numbers in all arithmetic progressions with first term and difference coprime