Counting Primes in Residue Classes

Abstract : We explain how the Meissel-Lehmer-Lagarias-Miller-Odlyzko method for computing π(x), the number of primes up to x, can be used for computing efficiently π(x,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 π(x,4,3) is less than π(x,4,1) near x=10^18.
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Submitted on : Thursday, September 19, 2013 - 10:18:25 AM
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Marc Deléglise, Pierre Dusart, Xavier-François Roblot. Counting Primes in Residue Classes. Mathematics of Computation, American Mathematical Society, 2004, 73 (247), pp.1565-1575. ⟨hal-00863138⟩



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