素数の間隔
出典: フリー百科事典『ウィキペディア（Wikipedia）』 (2024/02/11 11:37 UTC 版)
素数の間隔（そすうのかんかく、prime gap）は、連続する2つの素数の差。gn もしくは g(pn) で表される n 番目の素数の間隔は、n + 1 番目の素数と n 番目の素数の差である。すなわち
- ^ "Hidden structure in the randomness of the prime number sequence?", S. Ares & M. Castro, 2005
- ^ オンライン整数列大辞典の数列 A001223
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- ^ Dynamic prime gap statistics
- ^ TABLES OF PRIME GAPS
- ^ 他の記録はA111943で見ることができる。
- ^ NEW MAXIMAL PRIME GAPS OF 1530 AND 1550
- ^ 他の記録はA005250にあり、A002386の対応する素数pnとA005669のnの値とともに見ることができる。
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- ^ 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.
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- ^ 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.
- ^ “Long gaps between primes / What's new”. 2020年3月閲覧。
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- ^ 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.
- ^ a b Guy (2004) §A8
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