KnowraElliott–Halberstam conjectureLinked fromLinked fromThe 5 pages that link to Elliott–Halberstam conjecture, each with the reason it gives.All 5Related 3Compared with 2Prime gapsRelated: Stronger distribution estimates could improve what is known about small recurring gaps.Sieve theoryRelated: Stronger distribution could let sieve arguments establish tighter bounds on prime gaps.Prime number theorem for arithmetic progressionsCompared with: It predicts substantially greater average uniformity than currently proven estimates.Bombieri–Vinogradov theoremCompared with: It predicts average control beyond the square-root barrier.Hardy–Littlewood conjecturesRelated: Stronger distribution estimates of this kind would support progress on prime-pattern questions.