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DENSITY AND DISTRIBUTION OF PRIMES
JP Journal of Algebra, Number Theory and Applications, 2020Summary: We study the distribution and density of primes depending on the computations which have been carried out on GAP (Groups, Algorithms, Programming -- a System for Computational Discrete Algebra).
Ibrahim, Mohammed Ali Faya +1 more
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On the Distribution of Supersingular Primes
Canadian Journal of Mathematics, 1996AbstractLet E be a fixed elliptic curve defined over the rational numbers. We prove that the number of primes p ≤ x such that E has supersingular reduction mod p is greater than for any positive δ and x sufficiently large. Here logkx is defined recursively as log(logk-1 x) and log1x = logx. We also establish several results related to the Lang-Trotter
Fouvry, Etienne, Murty, M. Ram
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Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, 1985
Let \({\mathcal F}\) denote the convolution semigroup of probability distributions on the real line. We prove that no element of \({\mathcal F}\) is prime in the sense that given an \(F\in {\mathcal F}\) one can always find two distributions G,H\(\in {\mathcal F}\) such that F is a convolution factor of G*H but neither of G nor of H.
Ruzsa, I. Z., Székely, G. J.
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Let \({\mathcal F}\) denote the convolution semigroup of probability distributions on the real line. We prove that no element of \({\mathcal F}\) is prime in the sense that given an \(F\in {\mathcal F}\) one can always find two distributions G,H\(\in {\mathcal F}\) such that F is a convolution factor of G*H but neither of G nor of H.
Ruzsa, I. Z., Székely, G. J.
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ON THE DISTRIBUTION OF PRIMES (mod4)
Analysis, 1995Chebyshev in 1853 conjectured that ``there are more primes \(\equiv 3\pmod 4\) than \(\equiv 1\pmod 4\)''. Let \(N(T)\) denote the number of integers \(m\leq T\) for which \(\pi(m; 4,1)> \pi(m; 4,3)\). The assertion of Knapowski and Turan that \(\lim_{T\to \infty} N(T)/ T=0\) was recently disproved by the author assuming the GRH.
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The Mathematics Teacher, 2003
he distribution of primes throughout the natural numbers is a wonderful mystery that has always entertained mathematicians—professional and amateur, genius and ordinary—yet complete understanding has eluded their attempts. The names of those who have considered the problems discussed in this article and related problems form a “mathematics hall of fame”
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he distribution of primes throughout the natural numbers is a wonderful mystery that has always entertained mathematicians—professional and amateur, genius and ordinary—yet complete understanding has eluded their attempts. The names of those who have considered the problems discussed in this article and related problems form a “mathematics hall of fame”
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Prime (distributive) fuzzy posets
Journal of Intelligent & Fuzzy Systems, 2019Fuzzy posets can be regarded as a generalization of classical posets. Many concepts and results in posets can be generalized to fuzzy posets. In order to further improve the fuzzy poset theory, in this paper, we shall introduce the concept of prime (distributive) fuzzy posets which can be seen as the correspondence of prime (distributive) posets in ...
Rongrong Wang, Shengwei Han
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Limitations to the equi-distribution of primes. IV
Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences, 1989Abstract We construct infinitely many different polynomials of given degree which take either significantly more or significantly less prime values than expected.
Friedlander, John, Granville, Andrew
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The Distribution of the Primes
1980Legendre was the first, as far as we know, to make any significant conjecture about the distribution of the primes. Let π(x) denote the number of primes not exceeding x. Then Legendre conjectured, somewhat tentatively, that for large x the number π(x) is given approximately by $$ \frac{x}{{\log x - 1.08...}} $$ .
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1984
How are the primes distributed among the integers? Here “distribution” is a misleading term because a given positive integer either is a prime or is not a prime — there is nothing chancy about primality. Yet superficially, the occurrence of primes appears to be rather haphazard, and, indeed, many properties can be derived by playing “dumb” and assuming
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How are the primes distributed among the integers? Here “distribution” is a misleading term because a given positive integer either is a prime or is not a prime — there is nothing chancy about primality. Yet superficially, the occurrence of primes appears to be rather haphazard, and, indeed, many properties can be derived by playing “dumb” and assuming
openaire +1 more source