Small gaps between products of two primes
By D. Goldston, S. Graham, Janos Pintz, C. Y. Yıldırım. 2006
78 citations recorded by the source corpus.
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.
Subfields: Algebra and Number Theory, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/758779b3914830f972a599fc1ce68a9f0d8b2ea3
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In Algebra and Number Theory
In Geometry and Topology
Citations in the corpus
- Small gaps between primes (2013, background): “This is [3, Lemma 4], with κ = 1 and slight changes to the notation.”