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Conjecture

Second Hardy-Littlewood Conjecture

Number Theory

The second Hardy-Littlewood conjecture, in number theory, concerns the number of primes found in intervals of the positive integers. Along with the related first Hardy-Littlewood conjecture, it was proposed by G. H. Hardy and John Edensor Littlewood in 1923. 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
pi(x+y) <= pi(x) + pi(y) for integers x, y >= 2, where pi is the prime-counting function. 1
Proposed Year
1923 1
Progress Toward Resolution
Shown to be inconsistent with the first Hardy-Littlewood conjecture on prime k-tuples; the first violation is expected only at very large values of x. 1
Classification
Resolution Status
Open 1
Prize Status
Prize Status (category)
No Prize Offered 1
Connections

In Branch

Number Theory, Branches of Mathematics
Source Second Hardy-Littlewood conjecture (Wikipedia)
Sources
1. Second Hardy-Littlewood Conjecture (Wikipedia)
Wikimedia Foundation
  • Lead section
    the second Hardy-Littlewood conjecture was proposed by G. H. Hardy and John Edensor Littlewood in 1923
  • Connection to the first Hardy-Littlewood conjecture, first sentence
    The statement of the second Hardy-Littlewood conjecture is equivalent to the statement that the number of primes from x + 1 to x + y is always less than or equal to the number of primes from 1 to y.
  • Connection to the first Hardy-Littlewood conjecture, second sentence
    This was proved to be inconsistent with the first Hardy-Littlewood conjecture on prime k-tuples
View the Source
Second Hardy-Littlewood conjecture (Wikipedia)
In Branch: Number Theory, Lead sentenceView the Source
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