Let be the smallest Prime in the arithmetic progression for an Integer . Let

such that and . Then there exists a and an such that for all . is known as Linnik's Constant.

**References**

Linnik, U. V. ``On the Least Prime in an Arithmetic Progression. I. The Basic Theorem.''
*Mat. Sbornik N. S.* **15 (57)**, 139-178, 1944.

Linnik, U. V. ``On the Least Prime in an Arithmetic Progression. II. The Deuring-Heilbronn Phenomenon''
*Mat. Sbornik N. S.* **15 (57)**, 347-368, 1944.

© 1996-9

1999-05-25