##  [Dirichlet's Theorem on Primes in Arithmetic Progressions](/dirichlets-theorem-primes-arithmetic-progressions) 

  ##  [Dirichlet's Theorem on Primes in Arithmetic Progressions](https://puremath.quantumdictionary.io/dirichlets-theorem-primes-arithmetic-progressions-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The theorem that any arithmetic progression a, a+d, a+2d, ... with gcd(a,d)=1 contains infinitely many prime numbers; it guarantees at least one prime in infinitely many positions of the progression when the initial term and modulus are coprime.