一種改進的 Miller 素性測試，可以保證素性或合性。對於數字 
，該演算法的執行時間已被證明為 
，其中 
。它由 Cohen 和 Lenstra (1984) 簡化，由 Cohen 和 Lenstra (1987) 實現，隨後由 Bosma 和 van der Hulst (1990) 最佳化。
Adleman-Pomerance-Rumely 素性測試
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Miller 素性測試使用 探索
參考文獻
Adleman, L. M.; Pomerance, C.; and Rumely, R. S. "On Distinguishing Prime Numbers from Composite Number." Ann. Math. 117, 173-206, 1983.Bosma, W. and van der Hulst, M.-P. "Faster Primality Testing." In Advances in Cryptology, Proc. Eurocrypt '89, Houthalen, April 10-13, 1989 (Ed. J.-J. Quisquater). New York: Springer-Verlag, 652-656, 1990.Brillhart, J.; Lehmer, D. H.; Selfridge, J.; Wagstaff, S. S. Jr.; and Tuckerman, B. Factorizations of b-n+/-1, b=2, 3, 5, 6, 7, 10, 11, 12 Up to High Powers, rev. ed. Providence, RI: Amer. Math. Soc., pp. lxxxiv-lxxxv, 1988.Cohen, H. and Lenstra, A. K. "Primality Testing and Jacobi Sums." Math. Comput. 42, 297-330, 1984.Cohen, H. and Lenstra, A. K. "Implementation of a New Primality Test." Math. Comput. 48, 103-121, 1987.Mihailescu, P. "A Primality Test Using Cyclotomic Extensions." In Applied Algebra, Algebraic Algorithms and Error-Correcting Codes: Proceedings of the Sixth International Conference (AAECC-6) held in Rome, July 4-8, 1988 (Ed. T. Mora). New York: Springer-Verlag, pp. 310-323, 1989.在 中被引用
Adleman-Pomerance-Rumely 素性測試請引用為
Weisstein, Eric W. "Adleman-Pomerance-Rumely 素性測試。" 來自 Web 資源。 https://mathworld.tw/Adleman-Pomerance-RumelyPrimalityTest.html