#### Top 20 Arithmetic Progression of Primes

by Chris Caldwell

The Prime Pages keeps a list of the 5000 largest known primes, plus a few each of certain selected archivable forms and classes. These forms are defined in this collection’s home page. This page is about one of those forms.

** Definitions and Notes**

Are there infinitely many primes in most arithmetic progressions? Certainly not if the common difference has a prime factor in common with one of the terms (for example: 6, 9, 12, 15, …). In 1837, Dirichlet proved that in all other cases the answer was yes:

Dirichlet’s Theorem on Primes in Arithmetic Progressions- If
aandbare relatively prime positive integers, then the arithmetic progressiona,a+b,a+2b,a+3b, … contains infinitely many primes.

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