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 a and b are relatively prime positive integers, then the arithmetic progression a, a+b, a+2b, a+3b, … contains infinitely many primes.
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