Summary
A new algorithm is presented for finding all primes between 2 and an incrementally increasing value n. The algorithm executes in linear arithmetic time and space. An outline is given to show how previously developed techniques can be applied to improve the efficiency of the algorithm to O(n/loglogn) time and space.
Similar content being viewed by others
References
Aho, A.V., Hopcroft, J.E., Ullman, J.D.: The Design and Analysis of Computer Algorithms. Reading, MA: Addison-Wesley 1974
Bengelloun, S.A.: Balancing for Fixed Sequence Incremental Problems. (To be submitted for publication)
Bengelloun, S.A.: An Incremental Evaluator. (In preparation)
Bengelloun, S.A.: A New Variation on a Scheme of Eratosthenes. Technical Report, Dept. of Mathematics and Computer Science, Mahammad V University, Rabat, Morocco
Friedman, D., Wise, D.: CONS Should Not Evaluate Its Arguments. In: Automata, Languages, and Programming, pp. 257–284. Edinburgh: University Press 1976
Gries, D., Misra, J.: A Linear Sieve Algorithm for Finding Prime Numbers. Commun. A. C. M. 21, 999–1003 (1978)
Hardy, G.H., Wright, E.M.: An Introduction to the Theory of Numbers. New York: Oxford University Press 1960
Henderson, P., Morris, J. (Jr.): A Lazy Evaluator. In Third Annual Symposium on Principles of Programming Languages, pp. 95–103. Association for Computing Machinery 1976
Mairson, H.G.: Some New Upper Bounds on the Generation of Prime Numbers. Commun. ACM 20, 664–669 (1977)
Monier, L.: Algorithmes de Factorisation d'Entiers. PhD Thesis, l'Universite Paris-Sud, Centre d'Orsay, 1980
Pritchard, P.: A Sublinear Additive Sieve for Finding Prime Numbers. Commun. ACM 24, 18–23 (1981)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Bengelloun, S.A. An incremental primal sieve. Acta Informatica 23, 119–125 (1986). https://doi.org/10.1007/BF00289493
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00289493