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Episode 477

Linnik's theorem
Fri, 2018-Aug-24 00:06 UTC
Length - 1:51

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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






{\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:












{\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

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These podcasts are produced by Abulsme Productions based on Wikipedia content.

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Abulsme Productions also produces Curmudgeon's Corner, a current events podcast.

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