TOPICS
Search

Linnik's Theorem

Let p(d,a) be the smallest prime in the arithmetic progression {a+kd} for k an integer >0. Let

p(d)=maxp(d,a)

such that 1<=a<d and (a,d)=1. Then there exists a d_0>=2 and an L>1 such that p(d)<d^L for all d>d_0. L is known as Linnik's constant.

See also

Arithmetic Progression, Linnik's Constant

Explore with Wolfram|Alpha

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.

Referenced on Wolfram|Alpha

Linnik's Theorem

Cite this as:

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

Subject classifications