prime quadruplet conjecture

Conjecture. (Hardy & Littlewood) There are infinitely many prime quadrupletsMathworldPlanetmath.

As with twin primesMathworldPlanetmath, prime quadruplets generally become scarcer the higher one looks for them with the aid of the computer, yet they also display the same unevenness of distributionPlanetmathPlanetmath: there is only one prime quadruplet between 40000 and 50000, yet there are three between 70000 and 80000. While Euclid proved long ago that there are infinitely many primes, it is still not known whether there are also infinitely many prime quadruplets.

The question is related to the twin prime conjecture: proving the prime quadruplet conjecture would automatically prove the twin prime conjecture as well. However, disproving the prime quadruplet conjecture might not necessarily disprove the twin prime conjecture as well.

Hardy and Littlewood stated their conjecture in more general terms as the prime k-tuple conjecture, with the case of the prime quadruplets being for k=4.

Title prime quadruplet conjecture
Canonical name PrimeQuadrupletConjecture
Date of creation 2013-03-22 19:00:38
Last modified on 2013-03-22 19:00:38
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 5
Author PrimeFan (13766)
Entry type Conjecture
Classification msc 11N05