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1 ICJ - Institut Camille Jordan Villeurbanne 2 LACO - Laboratoire d-Arithmétique, de Calcul formel et d-Optimisation 3 IGD - Institut Girard Desargues

Abstract : We explain how the Meissel-Lehmer-Lagarias-Miller-Odlyzko method for computing πx, the number of primes up to x, can be used for computing efficiently πx,k,l, the number of primes congruent to l modulo k up to x. As an application, we computed the number of prime numbers of the form 4n±1 less than x for several values of x up to 10^20 and found a new region where πx,4,3 is less than πx,4,1 near x=10^18.





Author: Marc Deléglise - Pierre Dusart - Xavier-François Roblot -

Source: https://hal.archives-ouvertes.fr/



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