Partitions in the prime number maze
Power values of certain quadratic polynomials
In this article we compute the th power values of the quadratic polynomials with negative squarefree discriminant such that is coprime to the class number of the splitting field of over . The theory of unique factorisation and that of primitive divisors of integer sequences is used to deduce a bound on the values of which is small enough to allow the remaining cases to be easily checked. The results are used to determine all perfect power terms of certain polynomially generated integer...
Primality testing algorithms
Prime divisors of polynomials at consecutive integers.
Prime facto rs of consecutive integers.
Prime factors of binomial coefficients and related problems
Prime numbers with a fixed number of one bits or zero bits in their binary representation.
Prime Pythagorean triangles.
Prime values of irreducible polynomials
Primes in Fibonacci -step and Lucas -step sequences.
Primes in intervals
Primitive prime divisors in polynomial arithmetic dynamics.
Primzahlen.
Progressions arithmétiques dans les nombres premiers
Récemment, B. Green et T. Tao ont montré que : l’ensemble des nombres premiers contient des progressions arithmétiques de toutes longueurs répondant ainsi à une question ancienne à la formulation particulièrement simple. La démonstration n’utilise aucune des méthodes “transcendantes” ni aucun des grands théorèmes de la théorie analytique des nombres. Elle est écrite dans un esprit proche de celui de la théorie ergodique, en particulier de celui de la preuve par Furstenberg du théorème de Szemerédi,...
Properties of non powerful numbers.
Prvočísla obsahují libovolně dlouhé aritmetické posloupnosti
Quelques applications de nouveaux résultats de van der Poorten
Ramanujan primes: bounds, runs, twins, and gaps.
Rekurrente Folgen mit lokal gleichmäßig beschränkter Primteileranzahl
Remarks on Ramanujan's inequality concerning the prime counting function
In this paper we investigate Ramanujan’s inequality concerning the prime counting function, asserting that for sufficiently large. First, we study its sharpness by giving full asymptotic expansions of its left and right hand sides expressions. Then, we discuss the structure of Ramanujan’s inequality, by replacing the factor on its right hand side by the factor for a given , and by replacing the numerical factor by a given positive . Finally, we introduce and study inequalities analogous...