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- Publisher
- Springer Journals
- Copyright
- Copyright © 2014 by Polymath; licensee Springer.
- Subject
- Mathematics; Mathematics, general; Applications of Mathematics; Computational Mathematics and Numerical Analysis
- eISSN
- 2197-9847
- DOI
- 10.1186/s40687-014-0012-7
- Publisher site
- See Article on Publisher Site
Abstract
For any m≥1, let H m denote the quantity liminf n → ∞ ( p n + m − p n ) . A celebrated recent result of Zhang showed the finiteness of H 1, with the explicit bound H 1≤70,000,000. This was then improved by us (the Polymath8 project) to H 1≤4680, and then by Maynard to H 1≤600, who also established for the first time a finiteness result for H m for m≥2, and specifically that H m ≪m 3 e 4m . If one also assumes the Elliott-Halberstam conjecture, Maynard obtained the bound H 1≤12, improving upon the previous bound H 1≤16 of Goldston, Pintz, and Yıldırım, as well as the bound H m ≪m 3 e 2m .
Journal
Research in the Mathematical Sciences – Springer Journals
Published: Oct 17, 2014