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Conjecture

Bateman-Horn Conjecture

Number Theory

The Bateman-Horn conjecture, in number theory, is a statement concerning the frequency of prime numbers among the values of a system of polynomials. It was proposed by Paul T. Bateman and Roger A. Horn in 1962 and provides a vast generalization of conjectures such as the Hardy-Littlewood conjecture on the density of twin primes and on primes of the form n squared plus one; it is also a strengthening of Schinzel's hypothesis H. 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
Statement
The Bateman-Horn conjecture gives a conjectured density for the positive integers at which a given set of irreducible integer polynomials all have prime values. 1
Proposed Year
1962 1
Classification
Resolution Status
Open 1
Prize Status
Prize Status (category)
No Prize Offered 1
Connections

In Branch

Number Theory, Branches of Mathematics
Source Bateman-Horn conjecture (Wikipedia)
Sources
1. Bateman-Horn Conjecture (Wikipedia)
Wikimedia Foundation
  • Lead section
    named after mathematicians Paul T. Bateman and Roger A. Horn who proposed it in 1962
  • Definition
    The Bateman-Horn conjecture provides a conjectured density for the positive integers at which a given set of polynomials all have prime values.
View the Source
Bateman-Horn conjecture (Wikipedia)
In Branch: Number Theory, Lead sentenceView the Source
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