The Elliott-Halberstam conjecture, in number theory, concerns the distribution of prime numbers in arithmetic progressions and has many applications in sieve theory. It is named for Peter D. T. A. Elliott and Heini Halberstam, who stated a specific version of the conjecture in 1968; Bombieri and Vinogradov proved a weaker averaged form, and the conjecture is known to fail at its strongest endpoint, but the full conjecture remains open. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/
Facts
Proposed Year Progress Toward ResolutionProven in the averaged range below one half by Bombieri and Vinogradov (Bombieri-Vinogradov theorem), known to fail at the endpoint where theta equals 1, and open in between. 1 Classification
Resolution Status Prize Status
Prize Status (category) Connections
In Branch
Source Elliott-Halberstam Conjecture (Wikipedia)
Sources
1. Elliott-Halberstam Conjecture (Wikipedia)
Wikimedia FoundationLead section
who stated a specific version of the conjecture in 1968
Lead section, third paragraph
It is known that the conjecture fails at the endpoint
- In Branch: Number Theory, Lead sentence
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