Given an Arithmetic Series of terms , for , 2, ..., the series contains an infinite number of Primes if and are Relatively Prime, i.e., . Dirichlet proved this theorem using Dirichlet L-Series.
See also Prime Arithmetic Progression, Prime Patterns Conjecture, Relatively Prime, Sierpinski's Prime Sequence Theorem
References
Courant, R. and Robbins, H. ``Primes in Arithmetical Progressions.'' §1.2b in Supplement to Ch. 1 in
What is Mathematics?: An Elementary Approach to Ideas and Methods, 2nd ed.
Oxford, England: Oxford University Press, pp. 26-27, 1996.
Shanks, D. Solved and Unsolved Problems in Number Theory, 4th ed. New York: Chelsea, pp. 22-23, 1993.