In the preprint [3], Goldston, Pintz, and Yıldırım established, among other things, {equation} n→∞{pₙ₊₁-p_nlog p_n}=0, {equation} with pₙ the nth prime. In the present article, which is essentially self-contained, we shall develop a simplified account of the method used in [3]. We include a short expository last section.
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Goldston et al. (2006) studied this question.
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