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Prime Sieves Using Binary Quadratic Forms (1999) [7 citations — 1 self]

by A. O. L. Atkin ,  D. J. Bernstein
Mathematics of Computation
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Abstract:

. We introduce an algorithm that computes the prime numbers up to N using O(N=log log N) additions and N 1=2+o(1) bits of memory. The algorithm enumerates representations of integers by certain binary quadratic forms. We present implementation results for this algorithm and one of the best previous algorithms. 1.

Citations

58 Algebraic number theory – Cassels, Frohlich - 1967
45 An Introduction to the Theory of Numbers, 5th Edition – Hardy, Wright - 1979
16 A linear algorithm for incremental digital display of circular arcs – Bresenham - 1977
9 Fast compact prime number sieves (among others – Pritchard - 1983
8 The first occurrence of large gaps between successive primes – Brent - 1973
6 Zen of graphics programming – Abrash - 1995
6 The segmented sieve of Eratosthenes and primes in arithmetic progressions to 10 – Bays, Hudson - 1977
5 Explaining the wheel sieve – Pritchard - 1982
2 Experiments on the lattice problem – Keller, Swenson - 1963
2 Elementary number theory, McGraw-Hill – Uspensky, Heaslet - 1939
1 A space-ecient fast prime number sieve – Dunten, Jones, et al. - 1996
1 A sublinear additive sieve for prime numbers – Pritchard - 1981
1 Algorithm 356: a prime number generator using the treesort principle – Singleton - 1969
1 Algorithm 357: an ecient prime number generator – Singleton - 1969
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