On limit points of the sequence of normalized prime gaps. Issue 4 (23rd August 2016)

• Record Type: Journal Article
• Authors: Banks, William D.; Freiberg, Tristan; Maynard, James
• Is Part Of: Proceedings of the London Mathematical Society. Volume 113:Issue 4(2016:Oct.)
• Page Start: 515
• Page End: 539
• Publication Date: 2016-08-23
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals; 510
• DOI: 10.1112/plms/pdw036
• Languages: English
• ISSNs: 0024-6115

Abstract

Abstract : Letp n denote then th smallest prime number, and letL denote the set of limit points of the sequence{ ( p n + 1 − p n ) / log p n } n = 1 ∞ of normalized differences between consecutive primes. We show that, for any sequence of nine nonnegative real numbersβ 1 ⩽ β 2 ⩽ ⋯ ⩽ β 9, at least one of the numbersβ j − β i (1 ⩽ i < j ⩽ 9 ) belongs toL . It follows that at least12 . 5 % of all nonnegative real numbers belong toL .