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math.NT2020★ 2 cited
Small gaps between almost primes, the parity problem, and some conjectures of Erdős on consecutive integers II
Daniel A. Goldston, Sidney W. Graham, Apoorva Panidapu +3
This paper is intended as a sequel to a paper arXiv:0803.2636 written by four of the coauthors here. In the paper, they proved a stronger form of the Erdős-Mirksy conjecture which…
math.NT2008
Small gaps between almost primes, the parity problem, and some conjectures of Erdos on consecutive integers
D. A. Goldston, S. W. Graham, J. Pintz +1
In a previous paper, the authors proved that in any system of three linear forms satisfying obvious necessary local conditions, there are at least two forms that infinitely often a…
math.NT2006★ 59 cited
Small gaps between products of two primes
D. A. Goldston, S. W. Graham, J. Pintz +1
Let denote the number that is a product of exactly two distinct primes. We prove that This sharpens an earlier result…