Linnik,s Theorem
Let 
be the smallest prime in the arithmetic progression ![<span style=]()
{a+kd}" src="https://mathworld.wolfram.com/images/equations/LinniksTheorem/Inline2.gif" style="height:15px; width:50px" /> 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.
