Bounded gaps between primes

Polymath threads

• I just can’t resist: there are infinitely many pairs of primes at most 59470640 apart, Scott Morrison, 30 May 2013
• The prime tuples conjecture, sieve theory, and the work of Goldston-Pintz-Yildirim, Motohashi-Pintz, and Zhang, Terence Tao, 3 June 2013.
• Polymath proposal: bounded gaps between primes, Terence Tao, 4 June 2013.

Other relevant blog posts

• Bounded gaps between primes!, Emmanuel Kowalski, 21 May 2013.
• Bounded gaps between primes: some grittier details, Emmanuel Kowalski, 4 June 2013.
  • The slides from the talk mentioned in that post

MathOverflow

• Philosophy behind Yitang Zhang’s work on the Twin Primes Conjecture, 20 May 2013.
• Tightening Zhang’s bound (closed), 3 June 2013.
• Does Zhang’s theorem generalize to 3 or more primes in an interval of fixed length?, 3 June 2013.

Recent papers and notes

• Bounded gaps between primes, Yitang Zhang, to appear, Annals of Mathematics. Released 21 May, 2013.
• Notes on Zhang's prime gaps paper, Terence Tao, 1 June 2013.
• Polignac Numbers, Conjectures of Erdös on Gaps between Primes, Arithmetic Progressions in Primes, and the Bounded Gap Conjecture, Janos Pintz, 27 May 2013.
• Bounded prime gaps in short intervals, Johan Andersson, 3 June 2013.

Bibliography

• [GPY2009] Goldston, Daniel A.; Pintz, János; Yıldırım, Cem Y. Primes in tuples. I. Ann. of Math. (2) 170 (2009), no. 2, 819–862. arXiv
• [MP2008] Motohashi, Yoichi; Pintz, János A smoothed GPY sieve. Bull. Lond. Math. Soc. 40 (2008), no. 2, 298–310.