Small gaps between products of two primes
Small gaps between products of two primes
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DOI：
10.1112/plms/pdn046
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发表时间：
2006-09
影响因子：
1.8
通讯作者：
D. Goldston;Sidney W. Graham;J. Pintz;C. Y. Yıldırım
中科院分区：
文献类型：
--
作者：
D. Goldston;Sidney W. Graham;J. Pintz;C. Y. Yıldırım
设qn表示第n个恰好是两个不同素数的乘积的数。我们证明了qn+1 − qn <$6无限频繁。这使作者早期的结果更加尖锐，该结果用26代替了6。更一般地，我们证明了如果ν是任何正整数，则（qn+ν − qn）无穷频繁地<$ν eν − γ（1+o（1））。我们还证明了其他几个相关的结果表示的数正好有两个素因子的线性形式。
Let qn denote the nth number that is a product of exactly two distinct primes. We prove that qn+1 − qn ⩽ 6 infinitely often. This sharpens an earlier result of the authors, which had 26 in place of 6. More generally, we prove that if ν is any positive integer, then (qn+ν − qn) ⩽ ν eν − γ (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.