Polignac's conjecture, in number theory, was made by Alphonse de Polignac in 1849 and states that for any positive even number n, there are infinitely many prime gaps of size n. For n equal to 2 it is the twin prime conjecture; Yitang Zhang's 2013 breakthrough proved there are infinitely many prime gaps of some size below 70 million, and later work reduced that bound, though the conjecture itself remains unproven for any specific value of n. 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
StatementFor any positive even number n, there are infinitely many prime gaps of size n. 1 Proposed Year Progress Toward ResolutionNot proven or disproven for any given n; Zhang proved in 2013 infinitely many gaps of some size below 70,000,000, later reduced to 246 per the Polymath project. 1 Classification
Resolution Status Prize Status
Prize Status (category) Connections
In Branch
Source Polignac's Conjecture (Wikipedia)
Posed By
Sources
1. Polignac's Conjecture (Wikipedia)
Wikimedia FoundationLead section
Polignac's conjecture was made by Alphonse de Polignac in 1849
Lead section, statement
For any positive even number n, there are infinitely many prime gaps of size n.
Lead section, second paragraph
Although the conjecture has not yet been proven or disproven for any given value of n
In Branch: Number Theory, Lead sentence
In number theory, Polignac's conjecture was made by Alphonse de Polignac in 1849 and states: For any positive even number n, there
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