Linnik's Theorem -- from Wolfram MathWorld

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Linnik's Theorem

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:

Finch, S. R. "Linnik's Constant." §2.12 in Mathematical Constants. Cambridge, England: Cambridge University Press, pp. 127-130, 2003.

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.

CITE THIS AS:

Weisstein, Eric W. "Linnik's Theorem." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/LinniksTheorem.html