Open Access
Differences between prime numbers
William J. Ellison
- 01 Jan 1974
- Vol. 15, Iss: 1, pp 1-10
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TL;DR: In this paper, Delange-Pisot-Poitou et al. implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/conditions).
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Abstract: © Séminaire Delange-Pisot-Poitou. Théorie des nombres (Secrétariat mathématique, Paris), 1973-1974, tous droits réservés. L’accès aux archives de la collection « Séminaire Delange-Pisot-Poitou. Théorie des nombres » implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.
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Citations
On the Andrica and Cramer’s Conjectures. Mathematical connections between Number Theory and some sectors of String Theory
Michele Nardelli
- 18 Mar 2010
TL;DR: In this article, some mathematical connections between various sectors of string theory and number theory have been discussed, particularly the Cramer-Shank conjecture and the related differences between prime numbers.
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•Posted Content
Critical probabilistic characteristics of the cramér model for primes and arithmetical properties
TL;DR: In this article, it was shown that the Cramer model has incidences on the Prime Number Theorem, since it predicts that the error term is sensitive to subsequences, and that infinite sequences of primes are ultimately avoided by the 'primes' with probability 1.
1
Gaps between prime numbers
Adolf Hildebrand,Helmut Maier +1 more
- 01 Jan 1988
TL;DR: In this article, it was shown that for any fixed integer k and sufficiently large T the set of limit points of the sequence {(dn/logn,... Idn+k1l/ logn)} in the cube [0,T]k has Lebesgue measure > c(k)T', where c(t) is a positive constant depending only on k. This generalizes a result of Ricci and answers a question of Erd6s, who had asked to prove that the sequence has a finite limit point greater than 1.
References
The difference between consecutive prime numbers. II
R. A. Rankin
- 01 Jul 1940
TL;DR: In a previous paper as mentioned in this paper, we considered the problem of how far apart two consecutive primes can be and gave an interesting answer that is not trivial, or that is at all illuminating.
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