Xuedong Luo
Abstract
Based on the sieve of Eratosthenes, a faster and more compact algorithm is presented for finding all primes between 2 and N.
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Digital Library
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Index Terms
A practical sieve algorithm finding prime numbers
Reviews
Thomas Zeugmann
The author presents a sieve algorithm that determines all primes between 2 and N in time O( N log log N) with storage requirement O( N). Consequently, neglecting constant factors, this algorithm has the same complexity as Eratosthenes' sieve. The new algorithm, however, decreases the constants. This linear speedup is achieved by dealing with the elements 5, 7, 11, 3 i + 2, 3( i + 1) + 1, . . . , - N only, where i is odd. Moreover, this new algorithm is even more compact than Eratosthenes' sieve. Nevertheless, the paper would have been more readable if the author had used only one “programming language” to formulate the algorithms, or if he had been denotationally more precise. Finally, since he states that Pritchard's O( N/log log N) additive sieve algorithm has more theoretical than practical significance, it would have been better to compare the new algorithm with Pritchard's sieve instead of with Eratosthenes's.
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