In a previous paper, an algorithm was presented for the classical problem of finding all prime numbers up to a given limit. The algorithm was derived therein by transforming a prior algorithm in accordance with some essentially ad hoc observations on the problem.
The present paper complements the former by developing a simple mathematical framework, which leads to a smoother and more insightful derivation of the new algorithm, and which may be of independent interest to the number theorist.
KeywordsInformation System Operating System Data Structure Communication Network Information Theory
Unable to display preview. Download preview PDF.
- 1.Brent, R.P.: The first occurrence of large gaps between successive primes. Maths. of Comp. 27, 959–963 (1973)Google Scholar
- 2.Erdös, P., Penney, D.E., Pomerance, C: On a class of relatively prime sequences. J. Number Theory 10, 451–474 (1978)Google Scholar
- 3.Kanold, H.J.: Über Primzahlen in arithmetischen Folgen. Math. Ann. 156, 393–395 (1964); II, Math. Ann. 157, 358–362 (1965)Google Scholar
- 4.Lakatos, I.: Proofs and refutations. Cambridge: Cambridge University Press 1976Google Scholar
- 5.Le Veque, W.J.: Elementary theory of numbers. Reading, Ma: Addison-Wesley 1965Google Scholar
- 6.Misra, J.: An exercise in program explanation. ACM Trans. Program. Lang. Syst. 3, 104–109 (1981)Google Scholar
- 7.Pomerance, C.: A note on the least prime in an arithmetic progression. J. Number Theory 12, 218–223 (1980)Google Scholar
- 8.Pritchard, P.: A sublinear additive sieve for finding prime numbers. Comm. ACM 24, 18–23 (1981)Google Scholar
- 9.Pritchard, P.: Another look at the “longest ascending subsequence” problem. Acta Informat. 16, 87–91 (1981)Google Scholar
- 10.Sierpiński, W.: Elementary theory of numbers. Warsaw: Państwowe Wydawnictwo Naukowe 1964Google Scholar
- 11.Wunderlick, M.D., Selfridge, J.L.: A design for a number theory package with an optimized trial division routine. Commun. ACM 17, 272–277 (1974)Google Scholar