Prime gap (English Wikipedia)

Ares, Saul; Castro, Mario (February 1, 2006). "Hidden structure in the randomness of the prime number sequence?". Physica A: Statistical Mechanics and Its Applications. 360 (2): 285–296. arXiv:cond-mat/0310148. doi:10.1016/j.physa.2005.06.066. S2CID 16678116.
Kourbatov, A.; Wolf, M. (2020). "On the first occurrences of gaps between primes in a residue class". Journal of Integer Sequences. 23 (Article 20.9.3). arXiv:2002.02115. MR 4167933. S2CID 211043720. Zbl 1444.11191. Archived from the original on April 12, 2021. Retrieved December 3, 2020.
Cheng, Yuan-You Fu-Rui (2010). "Explicit estimate on primes between consecutive cubes". Rocky Mt. J. Math. 40: 117–153. arXiv:0810.2113. doi:10.1216/rmj-2010-40-1-117. S2CID 15502941. Zbl 1201.11111.
Goldston, Daniel A.; Pintz, János; Yıldırım, Cem Yalçin (2010). "Primes in Tuples II". Acta Mathematica. 204 (1): 1–47. arXiv:0710.2728. doi:10.1007/s11511-010-0044-9. S2CID 7993099.
Maynard, James (2015). "Small gaps between primes". Annals of Mathematics. 181 (1): 383–413. arXiv:1311.4600. doi:10.4007/annals.2015.181.1.7. MR 3272929. S2CID 55175056.
D.H.J. Polymath (2014). "Variants of the Selberg sieve, and bounded intervals containing many primes". Research in the Mathematical Sciences. 1 (12). arXiv:1407.4897. doi:10.1186/s40687-014-0012-7. MR 3373710. S2CID 119699189.
Ford, Kevin; Green, Ben; Konyagin, Sergei; Tao, Terence (2016). "Large gaps between consecutive prime numbers". Ann. of Math. 183 (3): 935–974. arXiv:1408.4505. doi:10.4007/annals.2016.183.3.4. MR 3488740. S2CID 16336889.
Maynard, James (2016). "Large gaps between primes". Ann. of Math. 183 (3): 915–933. arXiv:1408.5110. doi:10.4007/annals.2016.183.3.3. MR 3488739. S2CID 119247836.
Ford, Kevin; Green, Ben; Konyagin, Sergei; Maynard, James; Tao, Terence (2018). "Long gaps between primes". J. Amer. Math. Soc. 31 (1): 65–105. arXiv:1412.5029. doi:10.1090/jams/876. MR 3718451. S2CID 14487001.
Ford, Kevin; Maynard, James; Tao, Terence (October 13, 2015). "Chains of large gaps between primes". arXiv:1511.04468 [math.NT].
Sinha, Nilotpal Kanti (2010). "On a new property of primes that leads to a generalization of Cramer's conjecture". arXiv:1010.1399 [math.NT]..

books.google.com

Erdős, Paul; Bollobás, Béla; Thomason, Andrew, eds. (1997). Combinatorics, Geometry and Probability: A Tribute to Paul Erdős. Cambridge University Press. p. 1. ISBN 9780521584722. Archived from the original on September 29, 2022. Retrieved September 29, 2022.

dartmouth.edu

Granville, Andrew (1995). "Harald Cramér and the distribution of prime numbers" (PDF). Scandinavian Actuarial Journal. 1: 12–28. CiteSeerX 10.1.1.129.6847. doi:10.1080/03461238.1995.10413946. Archived (PDF) from the original on September 23, 2015. Retrieved March 2, 2016..

doi.org

Ares, Saul; Castro, Mario (February 1, 2006). "Hidden structure in the randomness of the prime number sequence?". Physica A: Statistical Mechanics and Its Applications. 360 (2): 285–296. arXiv:cond-mat/0310148. doi:10.1016/j.physa.2005.06.066. S2CID 16678116.
Heilbronn, H. A. (1933). "Über den Primzahlsatz von Herrn Hoheisel". Mathematische Zeitschrift. 36 (1): 394–423. doi:10.1007/BF01188631. JFM 59.0947.01. S2CID 123216472.
Ingham, A. E. (1937). "On the difference between consecutive primes". Quarterly Journal of Mathematics. Oxford Series. 8 (1): 255–266. Bibcode:1937QJMat...8..255I. doi:10.1093/qmath/os-8.1.255.
Cheng, Yuan-You Fu-Rui (2010). "Explicit estimate on primes between consecutive cubes". Rocky Mt. J. Math. 40: 117–153. arXiv:0810.2113. doi:10.1216/rmj-2010-40-1-117. S2CID 15502941. Zbl 1201.11111.
Huxley, M. N. (1972). "On the Difference between Consecutive Primes". Inventiones Mathematicae. 15 (2): 164–170. Bibcode:1971InMat..15..164H. doi:10.1007/BF01418933. S2CID 121217000.
Baker, R. C.; Harman, G.; Pintz, J. (2001). "The difference between consecutive primes, II". Proceedings of the London Mathematical Society. 83 (3): 532–562. CiteSeerX 10.1.1.360.3671. doi:10.1112/plms/83.3.532. S2CID 8964027.
Goldston, Daniel A.; Pintz, János; Yıldırım, Cem Yalçin (2010). "Primes in Tuples II". Acta Mathematica. 204 (1): 1–47. arXiv:0710.2728. doi:10.1007/s11511-010-0044-9. S2CID 7993099.
Zhang, Yitang (2014). "Bounded gaps between primes". Annals of Mathematics. 179 (3): 1121–1174. doi:10.4007/annals.2014.179.3.7. MR 3171761.
Maynard, James (2015). "Small gaps between primes". Annals of Mathematics. 181 (1): 383–413. arXiv:1311.4600. doi:10.4007/annals.2015.181.1.7. MR 3272929. S2CID 55175056.
D.H.J. Polymath (2014). "Variants of the Selberg sieve, and bounded intervals containing many primes". Research in the Mathematical Sciences. 1 (12). arXiv:1407.4897. doi:10.1186/s40687-014-0012-7. MR 3373710. S2CID 119699189.
Pintz, J. (1997). "Very large gaps between consecutive primes". J. Number Theory. 63 (2): 286–301. doi:10.1006/jnth.1997.2081.
Ford, Kevin; Green, Ben; Konyagin, Sergei; Tao, Terence (2016). "Large gaps between consecutive prime numbers". Ann. of Math. 183 (3): 935–974. arXiv:1408.4505. doi:10.4007/annals.2016.183.3.4. MR 3488740. S2CID 16336889.
Maynard, James (2016). "Large gaps between primes". Ann. of Math. 183 (3): 915–933. arXiv:1408.5110. doi:10.4007/annals.2016.183.3.3. MR 3488739. S2CID 119247836.
Ford, Kevin; Green, Ben; Konyagin, Sergei; Maynard, James; Tao, Terence (2018). "Long gaps between primes". J. Amer. Math. Soc. 31 (1): 65–105. arXiv:1412.5029. doi:10.1090/jams/876. MR 3718451. S2CID 14487001.
Cramér, Harald (1936). "On the order of magnitude of the difference between consecutive prime numbers". Acta Arithmetica. 2: 23–46. doi:10.4064/aa-2-1-23-46.
Ingham, Albert E. (1937). "On the difference between consecutive primes" (PDF). Quart. J. Math. 8 (1). Oxford: 255–266. Bibcode:1937QJMat...8..255I. doi:10.1093/qmath/os-8.1.255. Archived (PDF) from the original on December 5, 2022.
Granville, Andrew (1995). "Harald Cramér and the distribution of prime numbers" (PDF). Scandinavian Actuarial Journal. 1: 12–28. CiteSeerX 10.1.1.129.6847. doi:10.1080/03461238.1995.10413946. Archived (PDF) from the original on September 23, 2015. Retrieved March 2, 2016..
Granville, Andrew (1995). "Unexpected Irregularities in the Distribution of Prime Numbers" (PDF). Proceedings of the International Congress of Mathematicians. Vol. 1. pp. 388–399. doi:10.1007/978-3-0348-9078-6_32. ISBN 978-3-0348-9897-3. Archived (PDF) from the original on May 7, 2016. Retrieved March 2, 2016..
Pintz, János (September 2007). "Cramér vs. Cramér: On Cramér's probabilistic model for primes". Functiones et Approximatio Commentarii Mathematici. 37 (2): 232–471. doi:10.7169/facm/1229619660.

dustri.org

Ingham, Albert E. (1937). "On the difference between consecutive primes" (PDF). Quart. J. Math. 8 (1). Oxford: 255–266. Bibcode:1937QJMat...8..255I. doi:10.1093/qmath/os-8.1.255. Archived (PDF) from the original on December 5, 2022.

github.com

"Prime Gap Records". GitHub. June 11, 2022.

harvard.edu

ui.adsabs.harvard.edu

Ingham, A. E. (1937). "On the difference between consecutive primes". Quarterly Journal of Mathematics. Oxford Series. 8 (1): 255–266. Bibcode:1937QJMat...8..255I. doi:10.1093/qmath/os-8.1.255.
Huxley, M. N. (1972). "On the Difference between Consecutive Primes". Inventiones Mathematicae. 15 (2): 164–170. Bibcode:1971InMat..15..164H. doi:10.1007/BF01418933. S2CID 121217000.
Ingham, Albert E. (1937). "On the difference between consecutive primes" (PDF). Quart. J. Math. 8 (1). Oxford: 255–266. Bibcode:1937QJMat...8..255I. doi:10.1093/qmath/os-8.1.255. Archived (PDF) from the original on December 5, 2022.

lynchburg.edu

faculty.lynchburg.edu

Nicely, Thomas R. (2019). "NEW PRIME GAP OF MAXIMUM KNOWN MERIT". faculty.lynchburg.edu. Archived from the original on April 30, 2021. Retrieved September 29, 2022.
Nicely, Thomas R. (2019). "TABLES OF PRIME GAPS". faculty.lynchburg.edu. Archived from the original on November 27, 2020. Retrieved September 29, 2022.

mersenneforum.org

ATH (March 11, 2024). "Announcement at Mersenneforum.org". Mersenneforum.org. Archived from the original on March 12, 2024.

michaelnielsen.org

"Bounded gaps between primes". Polymath. Archived from the original on February 28, 2020. Retrieved July 21, 2013.

ntheory.org

"Record prime gap info". ntheory.org. Archived from the original on October 13, 2016. Retrieved September 29, 2022.

primegap-list-project.github.io

"Top 20 overall merits". Prime gap list. Archived from the original on July 27, 2022. Retrieved September 29, 2022.

primerecords.dk

Andersen, Jens Kruse. "The Top-20 Prime Gaps". Archived from the original on December 27, 2019. Retrieved June 13, 2014.
Andersen, Jens Kruse (March 8, 2013). "A megagap with merit 25.9". primerecords.dk. Archived from the original on December 25, 2019. Retrieved September 29, 2022.

psu.edu

citeseerx.ist.psu.edu

Baker, R. C.; Harman, G.; Pintz, J. (2001). "The difference between consecutive primes, II". Proceedings of the London Mathematical Society. 83 (3): 532–562. CiteSeerX 10.1.1.360.3671. doi:10.1112/plms/83.3.532. S2CID 8964027.
Granville, Andrew (1995). "Harald Cramér and the distribution of prime numbers" (PDF). Scandinavian Actuarial Journal. 1: 12–28. CiteSeerX 10.1.1.129.6847. doi:10.1080/03461238.1995.10413946. Archived (PDF) from the original on September 23, 2015. Retrieved March 2, 2016..

pzktupel.de

Andersen, Jens Kruse. "Record prime gaps". Retrieved May 9, 2024.

semanticscholar.org

api.semanticscholar.org

Ares, Saul; Castro, Mario (February 1, 2006). "Hidden structure in the randomness of the prime number sequence?". Physica A: Statistical Mechanics and Its Applications. 360 (2): 285–296. arXiv:cond-mat/0310148. doi:10.1016/j.physa.2005.06.066. S2CID 16678116.
Kourbatov, A.; Wolf, M. (2020). "On the first occurrences of gaps between primes in a residue class". Journal of Integer Sequences. 23 (Article 20.9.3). arXiv:2002.02115. MR 4167933. S2CID 211043720. Zbl 1444.11191. Archived from the original on April 12, 2021. Retrieved December 3, 2020.
Heilbronn, H. A. (1933). "Über den Primzahlsatz von Herrn Hoheisel". Mathematische Zeitschrift. 36 (1): 394–423. doi:10.1007/BF01188631. JFM 59.0947.01. S2CID 123216472.
Cheng, Yuan-You Fu-Rui (2010). "Explicit estimate on primes between consecutive cubes". Rocky Mt. J. Math. 40: 117–153. arXiv:0810.2113. doi:10.1216/rmj-2010-40-1-117. S2CID 15502941. Zbl 1201.11111.
Huxley, M. N. (1972). "On the Difference between Consecutive Primes". Inventiones Mathematicae. 15 (2): 164–170. Bibcode:1971InMat..15..164H. doi:10.1007/BF01418933. S2CID 121217000.
Baker, R. C.; Harman, G.; Pintz, J. (2001). "The difference between consecutive primes, II". Proceedings of the London Mathematical Society. 83 (3): 532–562. CiteSeerX 10.1.1.360.3671. doi:10.1112/plms/83.3.532. S2CID 8964027.
Goldston, Daniel A.; Pintz, János; Yıldırım, Cem Yalçin (2010). "Primes in Tuples II". Acta Mathematica. 204 (1): 1–47. arXiv:0710.2728. doi:10.1007/s11511-010-0044-9. S2CID 7993099.
Maynard, James (2015). "Small gaps between primes". Annals of Mathematics. 181 (1): 383–413. arXiv:1311.4600. doi:10.4007/annals.2015.181.1.7. MR 3272929. S2CID 55175056.
D.H.J. Polymath (2014). "Variants of the Selberg sieve, and bounded intervals containing many primes". Research in the Mathematical Sciences. 1 (12). arXiv:1407.4897. doi:10.1186/s40687-014-0012-7. MR 3373710. S2CID 119699189.
Ford, Kevin; Green, Ben; Konyagin, Sergei; Tao, Terence (2016). "Large gaps between consecutive prime numbers". Ann. of Math. 183 (3): 935–974. arXiv:1408.4505. doi:10.4007/annals.2016.183.3.4. MR 3488740. S2CID 16336889.
Maynard, James (2016). "Large gaps between primes". Ann. of Math. 183 (3): 915–933. arXiv:1408.5110. doi:10.4007/annals.2016.183.3.3. MR 3488739. S2CID 119247836.
Ford, Kevin; Green, Ben; Konyagin, Sergei; Maynard, James; Tao, Terence (2018). "Long gaps between primes". J. Amer. Math. Soc. 31 (1): 65–105. arXiv:1412.5029. doi:10.1090/jams/876. MR 3718451. S2CID 14487001.

terrytao.wordpress.com

Tao, Terence (December 16, 2014). "Long gaps between primes / What's new". Archived from the original on June 9, 2019. Retrieved August 29, 2019.

umontreal.ca

dms.umontreal.ca

Granville, Andrew (1995). "Unexpected Irregularities in the Distribution of Prime Numbers" (PDF). Proceedings of the International Congress of Mathematicians. Vol. 1. pp. 388–399. doi:10.1007/978-3-0348-9078-6_32. ISBN 978-3-0348-9897-3. Archived (PDF) from the original on May 7, 2016. Retrieved March 2, 2016..

uwaterloo.ca

cs.uwaterloo.ca

Kourbatov, A.; Wolf, M. (2020). "On the first occurrences of gaps between primes in a residue class". Journal of Integer Sequences. 23 (Article 20.9.3). arXiv:2002.02115. MR 4167933. S2CID 211043720. Zbl 1444.11191. Archived from the original on April 12, 2021. Retrieved December 3, 2020.

web.archive.org

ATH (March 11, 2024). "Announcement at Mersenneforum.org". Mersenneforum.org. Archived from the original on March 12, 2024.
Andersen, Jens Kruse. "The Top-20 Prime Gaps". Archived from the original on December 27, 2019. Retrieved June 13, 2014.
Andersen, Jens Kruse (March 8, 2013). "A megagap with merit 25.9". primerecords.dk. Archived from the original on December 25, 2019. Retrieved September 29, 2022.
Nicely, Thomas R. (2019). "NEW PRIME GAP OF MAXIMUM KNOWN MERIT". faculty.lynchburg.edu. Archived from the original on April 30, 2021. Retrieved September 29, 2022.
"Record prime gap info". ntheory.org. Archived from the original on October 13, 2016. Retrieved September 29, 2022.
Nicely, Thomas R. (2019). "TABLES OF PRIME GAPS". faculty.lynchburg.edu. Archived from the original on November 27, 2020. Retrieved September 29, 2022.
"Top 20 overall merits". Prime gap list. Archived from the original on July 27, 2022. Retrieved September 29, 2022.
Kourbatov, A.; Wolf, M. (2020). "On the first occurrences of gaps between primes in a residue class". Journal of Integer Sequences. 23 (Article 20.9.3). arXiv:2002.02115. MR 4167933. S2CID 211043720. Zbl 1444.11191. Archived from the original on April 12, 2021. Retrieved December 3, 2020.
"Bounded gaps between primes". Polymath. Archived from the original on February 28, 2020. Retrieved July 21, 2013.
Erdős, Paul; Bollobás, Béla; Thomason, Andrew, eds. (1997). Combinatorics, Geometry and Probability: A Tribute to Paul Erdős. Cambridge University Press. p. 1. ISBN 9780521584722. Archived from the original on September 29, 2022. Retrieved September 29, 2022.
Tao, Terence (December 16, 2014). "Long gaps between primes / What's new". Archived from the original on June 9, 2019. Retrieved August 29, 2019.
Ingham, Albert E. (1937). "On the difference between consecutive primes" (PDF). Quart. J. Math. 8 (1). Oxford: 255–266. Bibcode:1937QJMat...8..255I. doi:10.1093/qmath/os-8.1.255. Archived (PDF) from the original on December 5, 2022.
Granville, Andrew (1995). "Harald Cramér and the distribution of prime numbers" (PDF). Scandinavian Actuarial Journal. 1: 12–28. CiteSeerX 10.1.1.129.6847. doi:10.1080/03461238.1995.10413946. Archived (PDF) from the original on September 23, 2015. Retrieved March 2, 2016..
Granville, Andrew (1995). "Unexpected Irregularities in the Distribution of Prime Numbers" (PDF). Proceedings of the International Congress of Mathematicians. Vol. 1. pp. 388–399. doi:10.1007/978-3-0348-9078-6_32. ISBN 978-3-0348-9897-3. Archived (PDF) from the original on May 7, 2016. Retrieved March 2, 2016..

zbmath.org

Westzynthius, E. (1931), "Über die Verteilung der Zahlen die zu den n ersten Primzahlen teilerfremd sind", Commentationes Physico-Mathematicae Helsingsfors (in German), 5: 1–37, JFM 57.0186.02, Zbl 0003.24601.
Kourbatov, A.; Wolf, M. (2020). "On the first occurrences of gaps between primes in a residue class". Journal of Integer Sequences. 23 (Article 20.9.3). arXiv:2002.02115. MR 4167933. S2CID 211043720. Zbl 1444.11191. Archived from the original on April 12, 2021. Retrieved December 3, 2020.
Hoheisel, G. (1930). "Primzahlprobleme in der Analysis". Sitzunsberichte der Königlich Preussischen Akademie der Wissenschaften zu Berlin. 33: 3–11. JFM 56.0172.02.
Heilbronn, H. A. (1933). "Über den Primzahlsatz von Herrn Hoheisel". Mathematische Zeitschrift. 36 (1): 394–423. doi:10.1007/BF01188631. JFM 59.0947.01. S2CID 123216472.
Tchudakoff, N. G. (1936). "On the difference between two neighboring prime numbers". Mat. Sb. 1: 799–814. Zbl 0016.15502.
Cheng, Yuan-You Fu-Rui (2010). "Explicit estimate on primes between consecutive cubes". Rocky Mt. J. Math. 40: 117–153. arXiv:0810.2113. doi:10.1216/rmj-2010-40-1-117. S2CID 15502941. Zbl 1201.11111.