Counting Primes in Residue Classes
Deléglise, Marc ; Dusart, Pierre ; Roblot, Xavier-François
HAL, hal-00863138 / Harvested from HAL
Text on HAL
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.
Publié le : 2004-07-05
Classification:  [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT] 
@article{hal-00863138,
     author = {Del\'eglise, Marc and Dusart, Pierre and Roblot, Xavier-Fran\c cois},
     title = {Counting Primes in Residue Classes},
     journal = {HAL},
     volume = {2004},
     number = {0},
     year = {2004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00863138}
}

Deléglise, Marc; Dusart, Pierre; Roblot, Xavier-François. Counting Primes in Residue Classes. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00863138/