Small gaps between products of two primes

被引：24

作者：

Goldston, D. A. ^{[1
]}

Graham, S. W. ^{[2
]}

Pintz, J. ^{[3
]}

Yildirim, C. Y. ^{[4
,5
]}

机构：

[1] San Jose State Univ, Dept Math, San Jose, CA 95192 USA

[2] Cent Michigan Univ, Dept Math, Mt Pleasant, MI 48859 USA

[3] Hungarian Acad Sci, Renyi Math Inst, H-1364 Budapest, Hungary

[4] Bogazici Univ, Dept Math, TR-34342 Istanbul, Turkey

[5] Feza Gursey Enstitusu, TR-81220 Istanbul, Turkey

来源：

PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY | 2009年 / 98卷

关键词：

NUMBER; THEOREM;

D O I：

10.1112/plms/pdn046

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let q(n) denote the nth number that is a product of exactly two distinct primes. We prove that q(n+1) - q(n) <= 6 infinitely often. This sharpens an earlier result of the authors, which had 26 in place of 6. More generally, we prove that if nu is any positive integer, then (q(n+nu) - q(n)) <= nu e(nu - gamma) (1+o(1)) infinitely often. We also prove several other related results on the representation of numbers with exactly two prime factors by linear forms.

引用

页码：741 / 774

页数：34

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