Episode 477
Linnik's theorem
Fri, 2018-Aug-24 00:06 UTC
Length - 1:51
Direct Link
Welcome to random Wiki of the Day where we read the summary of a random Wikipedia page every day.
The random article for Friday, 24 August 2018 is Linnik's theorem.
Linnik's theorem in analytic number theory answers a natural question after Dirichlet's theorem on arithmetic progressions. It asserts that there exist positive c and L such that, if we denote p(a,d) the least prime in the arithmetic progression
a
+
n
d
,
{\displaystyle a+nd,\ }
where n runs through the positive integers and a and d are any given positive coprime integers with 1 ≤ a ≤ d - 1, then:
p
(
a
,
d
)
<
c
d
L
.
{\displaystyle p(a,d)<cd^{L}.\;}
The theorem is named after Yuri Vladimirovich Linnik, who proved it in 1944. Although Linnik's proof showed c and L to be effectively computable, he provided no numerical values for them.
This recording reflects the Wikipedia text as of 00:06 UTC on Friday, 24 August 2018.
For the full current version of the article, go to https://en.wikipedia.org/wiki/Linnik%27s_theorem.
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This has been Geraint. Thank you for listening to random Wiki of the Day.
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