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.
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