Open Access
April 2006 Small gaps between primes exist
Daniel Alan Goldston, Yoichi Motohashi, János Pintz, Cem Yalçın Yıldırım
Proc. Japan Acad. Ser. A Math. Sci. 82(4): 61-65 (April 2006). DOI: 10.3792/pjaa.82.61


In the preprint [3], Goldston, Pintz, and Yıldırım established, among other things, \begin{equation} \liminf_{n\to\infty}{p_{n+1}-p_n\over\log p_n}=0, \end{equation} with $p_n$ the $n$th 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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Daniel Alan Goldston. Yoichi Motohashi. János Pintz. Cem Yalçın Yıldırım. "Small gaps between primes exist." Proc. Japan Acad. Ser. A Math. Sci. 82 (4) 61 - 65, April 2006.


Published: April 2006
First available in Project Euclid: 2 May 2006

zbMATH: 1168.11041
MathSciNet: MR2222213
Digital Object Identifier: 10.3792/pjaa.82.61

Primary: 11N05
Secondary: 11P32

Keywords: prime number

Rights: Copyright © 2006 The Japan Academy

Vol.82 • No. 4 • April 2006
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