Science Fair Project Encyclopedia
Linnik's theorem
Linnik's theorem in analytic number theory answers a natural question after Dirichlet's theorem. It asserts that, if we denote p(a,d) the least prime in the arithmetic progression
- a + nd,
for integer n>0, where a and d are any given positive coprime integers that 1 ≤ a ≤ d, there exist positive c and L such that:
The Theorem is named after Yuri Vladimirovich Linnik (1915-1972) who proved it in 1944.
As of 1992 we know that the Linnik's constant L ≤ 5.5 but we can take L=2 for almost all integers d. It is also conjectured that:
10-26-2009 08:16:03
The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details
The contents of this article is licensed from www.wikipedia.org under the GNU Free Documentation License. Click here to see the transparent copy and copyright details