Prove that there exist infinitely primes p such that the decimal representation contain the digits 123456789.
(Excuse-me my bad English, I don't speak that language)
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I suppose you're expected to use Dirichlet's theorem on arithmetic progressions? Take a look at the following sequence:
Is it possible to prove this using the fact that diverges (where )?
Originally Posted by JoachimAgrell Is it possible to prove this using the fact that diverges (where )? No. Dirichlet's theorem on arithmetic progressions is much stronger than this statement. In fact, since , Dirichlet's theorem on arithemtic progressions assures us that diverges. That diverges is not enough!
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