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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.
Jerzy Kaczorowski
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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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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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The distribution of prime numbers
Russian Mathematical Surveys, 1990CONTENTS Introduction Chapter I. The Riemann zeta-function and its connection with primes § 1. Definition of and Euler's identity § 2. Continuation of to the half-plane § 3. Continuation of to the whole plane § 4. Functional properties of and § 5. Zeros of and primes § 6. Elementary theorems on the complex zeros of § 7. Theorems of de la Vallee Poussin
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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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The Distribution of Prime Numbers
1982In this chapter we give some basic results concerning the distribution of prime numbers. The reader will only require some knowledge of the calculus —this chapter is a first introduction to analytic number theory and we shall omit all the deeper investigations.
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