A performance analysis of a simple prime-testing algorithm

Author:
M. C. Wunderlich

Journal:
Math. Comp. **40** (1983), 709-714

MSC:
Primary 10A25; Secondary 10-04

MathSciNet review:
689483

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Abstract: This paper gives an empirical performance analysis of a prime-proving program designed and implemented by the author and J. L. Selfridge in 1974. The algorithm has been commonly referred to as the "down algorithm" because of its recursive characteristics. It is shown, among other things, that of the 2270 primes tested, 94

**[1]**John Brillhart, D. H. Lehmer, and J. L. Selfridge,*New primality criteria and factorizations of 2^{𝑚}±1*, Math. Comp.**29**(1975), 620–647. MR**0384673**, 10.1090/S0025-5718-1975-0384673-1**[2]**Michael A. Morrison and John Brillhart,*A method of factoring and the factorization of 𝐹₇*, Math. Comp.**29**(1975), 183–205. Collection of articles dedicated to Derrick Henry Lehmer on the occasion of his seventieth birthday. MR**0371800**, 10.1090/S0025-5718-1975-0371800-5**[3]**Michael O. Rabin,*Probabilistic algorithm for testing primality*, J. Number Theory**12**(1980), no. 1, 128–138. MR**566880**, 10.1016/0022-314X(80)90084-0**[4]**J. L. Selfridge and M. C. Wunderlich,*An efficient algorithm for testing large numbers for primality*, Proceedings of the Fourth Manitoba Conference on Numerical Mathematics (Winnipeg, Man., 1974) Utilitas Math., Winnipeg, Man., 1975, pp. 109–120. Congr. Numer., No. XII. MR**0369226****[5]**R. Solovay and V. Strassen,*A fast Monte-Carlo test for primality*, SIAM J. Comput.**6**(1977), no. 1, 84–85. MR**0429721****[6]**H. C. Williams,*Primality testing on a computer*, Ars Combin.**5**(1978), 127–185. MR**504864****[7]**Marvin C. Wunderlich & J. L. Selfridge, "A design for a number theory package with an optimized trial division routine,"*Comm. ACM*, v. 17, 1974, pp. 272-276.

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DOI:
https://doi.org/10.1090/S0025-5718-1983-0689483-8

Article copyright:
© Copyright 1983
American Mathematical Society