Bounded gaps between primes: Difference between revisions
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== Bibliography == | == Bibliography == | ||
* [FI1983] Fouvry, E.; Iwaniec, H. Primes in arithmetic progressions. Acta Arith. 42 (1983), no. 2, 197–218. [http://www.ams.org/mathscinet-getitem?mr=719249 MathSciNet] [http://matwbn.icm.edu.pl/ksiazki/aa/aa42/aa4226.pdf Article] | |||
* [FI1985] Friedlander, John B.; Iwaniec, Henryk, Incomplete Kloosterman sums and a divisor problem. With an appendix by Bryan J. Birch and Enrico Bombieri. Ann. of Math. (2) 121 (1985), no. 2, 319–350. [http://www.jstor.org/stable/1971175 JSTOR] | * [FI1985] Friedlander, John B.; Iwaniec, Henryk, Incomplete Kloosterman sums and a divisor problem. With an appendix by Bryan J. Birch and Enrico Bombieri. Ann. of Math. (2) 121 (1985), no. 2, 319–350. [http://www.jstor.org/stable/1971175 JSTOR] | ||
* [GPY2009] Goldston, Daniel A.; Pintz, János; Yıldırım, Cem Y. Primes in tuples. I. Ann. of Math. (2) 170 (2009), no. 2, 819–862. [http://arxiv.org/abs/math/0508185 arXiv] [http://www.ams.org/mathscinet-getitem?mr=2552109 MathSciNet] | * [GPY2009] Goldston, Daniel A.; Pintz, János; Yıldırım, Cem Y. Primes in tuples. I. Ann. of Math. (2) 170 (2009), no. 2, 819–862. [http://arxiv.org/abs/math/0508185 arXiv] [http://www.ams.org/mathscinet-getitem?mr=2552109 MathSciNet] | ||
* [GR1998] Gordon, Daniel M.; Rodemich, Gene Dense admissible sets. Algorithmic number theory (Portland, OR, 1998), 216–225, Lecture Notes in Comput. Sci., 1423, Springer, Berlin, 1998. [http://www.ams.org/mathscinet-getitem?mr=1726073 MathSciNet] [http://www.ccrwest.org/gordon/ants.pdf Article] | |||
* [HR1973] Hensley, Douglas; Richards, Ian, On the incompatibility of two conjectures concerning primes. Analytic number theory (Proc. Sympos. Pure Math., Vol. XXIV, St. Louis Univ., St. Louis, Mo., 1972), pp. 123–127. Amer. Math. Soc., Providence, R.I., 1973. [http://www.ams.org/mathscinet-getitem?mr=340194 MathSciNet] | * [HR1973] Hensley, Douglas; Richards, Ian, On the incompatibility of two conjectures concerning primes. Analytic number theory (Proc. Sympos. Pure Math., Vol. XXIV, St. Louis Univ., St. Louis, Mo., 1972), pp. 123–127. Amer. Math. Soc., Providence, R.I., 1973. [http://www.ams.org/mathscinet-getitem?mr=340194 MathSciNet] | ||
* [HR1973b] Hensley, Douglas; Richards, Ian, Primes in intervals. Acta Arith. 25 (1973/74), 375–391. [http://www.ams.org/mathscinet-getitem?mr=396440 MathSciNet] | * [HR1973b] Hensley, Douglas; Richards, Ian, Primes in intervals. Acta Arith. 25 (1973/74), 375–391. [http://www.ams.org/mathscinet-getitem?mr=396440 MathSciNet] | ||
Revision as of 10:11, 4 June 2013
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.
Code and data
- Github, Scott Morrison
- A mathematica notebook for finding k_0, Scott Morrison
- k-tuple pattern data, Thomas J Engelsma
Other relevant blog posts
- Marker lecture III: “Small gaps between primes”, Terence Tao, 19 Nov 2008.
- The Goldston-Pintz-Yildirim result, and how far do we have to walk to twin primes ?, Emmanuel Kowalski, 22 Jan 2009.
- Number Theory News, Peter Woit, 12 May 2013.
- Bounded Gaps Between Primes, Emily Riehl, 14 May 2013.
- Bounded gaps between primes!, Emmanuel Kowalski, 21 May 2013.
- Bounded gaps between primes: some grittier details, Emmanuel Kowalski, 4 June 2013.
MathOverflow
- Philosophy behind Yitang Zhang’s work on the Twin Primes Conjecture, 20 May 2013.
- A technical question related to Zhang’s result of bounded prime gaps, 25 May 2013.
- How does Yitang Zhang use Cauchy’s inequality and Theorem 2 to obtain the error term coming from the [math]\displaystyle{ S_2 }[/math] sum, 31 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.
Wikipedia
Recent papers and notes
- Bounded gaps between primes, Yitang Zhang, to appear, Annals of Mathematics. Released 21 May, 2013.
- Polignac Numbers, Conjectures of Erdös on Gaps between Primes, Arithmetic Progressions in Primes, and the Bounded Gap Conjecture, Janos Pintz, 27 May 2013.
- A poor man's improvement on Zhang's result: there are infinitely many prime gaps less than 60 million, T. S. Trudgian, 28 May 2013.
- The Friedlander-Iwaniec sum, É. Fouvry, E. Kowalski, Ph. Michel., May 2013.
- Notes on Zhang's prime gaps paper, Terence Tao, 1 June 2013.
- Bounded prime gaps in short intervals, Johan Andersson, 3 June 2013.
Media
- First proof that infinitely many prime numbers come in pairs, Maggie McKee, Nature, 14 May 2013.
Bibliography
- [FI1983] Fouvry, E.; Iwaniec, H. Primes in arithmetic progressions. Acta Arith. 42 (1983), no. 2, 197–218. MathSciNet Article
- [FI1985] Friedlander, John B.; Iwaniec, Henryk, Incomplete Kloosterman sums and a divisor problem. With an appendix by Bryan J. Birch and Enrico Bombieri. Ann. of Math. (2) 121 (1985), no. 2, 319–350. JSTOR
- [GPY2009] Goldston, Daniel A.; Pintz, János; Yıldırım, Cem Y. Primes in tuples. I. Ann. of Math. (2) 170 (2009), no. 2, 819–862. arXiv MathSciNet
- [GR1998] Gordon, Daniel M.; Rodemich, Gene Dense admissible sets. Algorithmic number theory (Portland, OR, 1998), 216–225, Lecture Notes in Comput. Sci., 1423, Springer, Berlin, 1998. MathSciNet Article
- [HR1973] Hensley, Douglas; Richards, Ian, On the incompatibility of two conjectures concerning primes. Analytic number theory (Proc. Sympos. Pure Math., Vol. XXIV, St. Louis Univ., St. Louis, Mo., 1972), pp. 123–127. Amer. Math. Soc., Providence, R.I., 1973. MathSciNet
- [HR1973b] Hensley, Douglas; Richards, Ian, Primes in intervals. Acta Arith. 25 (1973/74), 375–391. MathSciNet
- [MP2008] Motohashi, Yoichi; Pintz, János A smoothed GPY sieve. Bull. Lond. Math. Soc. 40 (2008), no. 2, 298–310. MathSciNet
- [MV1973] Montgomery, H. L.; Vaughan, R. C. The large sieve. Mathematika 20 (1973), 119–134. MathSciNet
- [R1974] Richards, Ian On the incompatibility of two conjectures concerning primes; a discussion of the use of computers in attacking a theoretical problem. Bull. Amer. Math. Soc. 80 (1974), 419–438. MathSciNet Article
- [S2007] K. Soundararajan, Small gaps between prime numbers: the work of Goldston-Pintz-Yıldırım. Bull. Amer. Math. Soc. (N.S.) 44 (2007), no. 1, 1–18. MathSciNet
