素数の間隔 (Japanese Wikipedia)

Analysis of information sources in references of the Wikipedia article "素数の間隔" in Japanese language version.

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16doi.org

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10arxiv.org

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6ams.org

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3oeis.org

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3zbmath.org

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3trnicely.net

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2primerecords.dk

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2harvard.edu

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1lynchburg.edu

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1ntheory.org

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1michaelnielsen.org

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1google.co.jp

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1umontreal.ca

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ams.org

mathscinet.ams.org

Zhang, Yitang (2014). “Bounded gaps between primes”. Annals of Mathematics 179 (3): 1121–1174. doi:10.4007/annals.2014.179.3.7. MR3171761.
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. MR3272929.
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. MR3373710.
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. MR3488740.
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. MR3488739.
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. MR3718451.

arxiv.org

"Hidden structure in the randomness of the prime number sequence?", S. Ares & M. Castro, 2005
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. Zbl 1201.11111.
Goldston, D. A.; Pintz, J.; Yildirim, C. Y. (2007). "Primes in Tuples II". arXiv:0710.2728 [math.NT]。
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. MR3272929.
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. MR3373710.
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. MR3488740.
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. MR3488739.
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. MR3718451.
Ford, Kevin; Maynard, James; Tao, Terence (13 October 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]。.

dartmouth.edu

Granville, Andrew (1995). “Harald Cramér and the distribution of prime numbers”. Scandinavian Actuarial Journal 1: 12–28. doi:10.1080/03461238.1995.10413946. .

doi.org

Heilbronn, H. A. (1933). “Über den Primzahlsatz von Herrn Hoheisel”. Mathematische Zeitschrift 36 (1): 394–423. doi:10.1007/BF01188631.
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. 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.
Baker, R. C.; Harman, G.; Pintz, J. (2001). “The difference between consecutive primes, II”. Proceedings of the London Mathematical Society 83 (3): 532–562. doi:10.1112/plms/83.3.532.
Zhang, Yitang (2014). “Bounded gaps between primes”. Annals of Mathematics 179 (3): 1121–1174. doi:10.4007/annals.2014.179.3.7. MR3171761.
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. MR3272929.
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. MR3373710.
Pintz, J. (1997). “Very large gaps between consecutive primes”. Journal of 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. MR3488740.
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. MR3488739.
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. MR3718451.
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.
Granville, Andrew (1995). “Harald Cramér and the distribution of prime numbers”. Scandinavian Actuarial Journal 1: 12–28. doi:10.1080/03461238.1995.10413946. .
Granville, Andrew (1995). “Unexpected irregularities in the distribution of prime numbers”. Proceedings of the International Congress of Mathematicians 1: 388–399. doi:10.1007/978-3-0348-9078-6_32. ISBN 978-3-0348-9897-3. .
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.

google.co.jp

books.google.co.jp

Erdős, Paul; Bollobás, Béla; Thomason, Andrew, eds (1997). Combinatorics, Geometry and Probability: A Tribute to Paul Erdös. Cambridge University Press. p. 1. ISBN 9780521584722

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.

icm.edu.pl

matwbn.icm.edu.pl

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.

lynchburg.edu

faculty.lynchburg.edu

“Some Results of Research in Computational Number Theory (NEW LARGEST KNOWN PRIME GAP)”. 2021年10月27日閲覧。

michaelnielsen.org

“Bounded gaps between primes”. Polymath. 2013年7月21日閲覧。

ntheory.org

Dynamic prime gap statistics

oeis.org

オンライン整数列大辞典の数列 A001223
他の記録はA111943で見ることができる。
他の記録はA005250にあり、A002386の対応する素数p_nとA005669のnの値とともに見ることができる。

primerecords.dk

“The Top-20 Prime Gaps”. 2014年6月13日閲覧。
“A proven prime gap of 1113106”. 2021年10月27日閲覧。

terrytao.wordpress.com

“Long gaps between primes / What's new”. 2020年3月閲覧。

trnicely.net

umontreal.ca

dms.umontreal.ca

Granville, Andrew (1995). “Unexpected irregularities in the distribution of prime numbers”. Proceedings of the International Congress of Mathematicians 1: 388–399. doi:10.1007/978-3-0348-9078-6_32. ISBN 978-3-0348-9897-3. .

zbmath.org

Westzynthius, E. (1931), “Über die Verteilung der Zahlen die zu den n ersten Primzahlen teilerfremd sind” (ドイツ語), Commentationes Physico-Mathematicae Helsingsfors 5: 1-37, JFM 57.0186.02, Zbl 0003.24601 .
Hoheisel, G. (1930). “Primzahlprobleme in der Analysis”. Sitzunsberichte der Königlich Preussischen Akademie der Wissenschaften zu Berlin 33: 3–11. JFM 56.0172.02.
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. Zbl 1201.11111.