Miller–Rabin primality test (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Miller–Rabin primality test" in English language version.

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14doi.org

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5harvard.edu

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ams.org

Jaeschke, Gerhard (October 1993), "On strong pseudoprimes to several bases" (PDF), Mathematics of Computation, 61 (204): 915–926, doi:10.2307/2153262, JSTOR 2153262
Zhang, Zhenxiang & Tang, Min (October 2003), "Finding strong pseudoprimes to several bases. II" (PDF), Mathematics of Computation, 72 (44): 2085–2097, Bibcode:2003MaCom..72.2085Z, doi:10.1090/S0025-5718-03-01545-X
Burthe Jr., Ronald J. (1996), "Further investigations with the strong probable prime test" (PDF), Mathematics of Computation, 65 (213): 373–381, Bibcode:1996MaCom..65..373B, doi:10.1090/S0025-5718-96-00695-3

mathscinet.ams.org

Artjuhov, M. M. (1966–1967), "Certain criteria for primality of numbers connected with the little Fermat theorem", Acta Arithmetica, 12: 355–364, MR 0213289
Robert Baillie; Samuel S. Wagstaff, Jr. (October 1980). "Lucas Pseudoprimes" (PDF). Mathematics of Computation. 35 (152): 1391–1417. doi:10.1090/S0025-5718-1980-0583518-6. MR 0583518.

arxiv.org

Sorenson, Jonathan; Webster, Jonathan (2015). "Strong Pseudoprimes to Twelve Prime Bases". Mathematics of Computation. 86 (304): 985–1003. arXiv:1509.00864. Bibcode:2015arXiv150900864S. doi:10.1090/mcom/3134. S2CID 6955806.

dartmouth.edu

math.dartmouth.edu

Carl Pomerance; John L. Selfridge; Samuel S. Wagstaff, Jr. (July 1980). "The pseudoprimes to 25 ⋅ 10⁹" (PDF). Mathematics of Computation. 35 (151): 1003–1026. doi:10.1090/S0025-5718-1980-0572872-7.
Damgård, I.; Landrock, P. & Pomerance, C. (1993), "Average case error estimates for the strong probable prime test" (PDF), Mathematics of Computation, 61 (203): 177–194, Bibcode:1993MaCom..61..177D, doi:10.2307/2152945, JSTOR 2152945
Alford, W. R.; Granville, A.; Pomerance, C. (1994), "On the difficulty of finding reliable witnesses", Algorithmic Number Theory (PDF), Lecture Notes in Computer Science, vol. 877, Springer-Verlag, pp. 1–16, doi:10.1007/3-540-58691-1_36, ISBN 978-3-540-58691-3

doi.org

Miller, Gary L. (1976), "Riemann's Hypothesis and Tests for Primality", Journal of Computer and System Sciences, 13 (3): 300–317, doi:10.1145/800116.803773, S2CID 10690396
Rabin, Michael O. (1980), "Probabilistic algorithm for testing primality", Journal of Number Theory, 12 (1): 128–138, doi:10.1016/0022-314X(80)90084-0
Carl Pomerance; John L. Selfridge; Samuel S. Wagstaff, Jr. (July 1980). "The pseudoprimes to 25 ⋅ 10⁹" (PDF). Mathematics of Computation. 35 (151): 1003–1026. doi:10.1090/S0025-5718-1980-0572872-7.
F. Arnault (August 1995). "Constructing Carmichael Numbers Which Are Strong Pseudoprimes to Several Bases". Journal of Symbolic Computation. 20 (2): 151–161. doi:10.1006/jsco.1995.1042.
Damgård, I.; Landrock, P. & Pomerance, C. (1993), "Average case error estimates for the strong probable prime test" (PDF), Mathematics of Computation, 61 (203): 177–194, Bibcode:1993MaCom..61..177D, doi:10.2307/2152945, JSTOR 2152945
Martin R. Albrecht; Jake Massimo; Kenneth G. Paterson; Juraj Somorovsky (15 October 2018). Prime and Prejudice: Primality Testing Under Adversarial Conditions (PDF). ACM SIGSAC Conference on Computer and Communications Security 2018. Toronto: Association for Computing Machinery. pp. 281–298. doi:10.1145/3243734.3243787.
Bach, Eric (1990), "Explicit bounds for primality testing and related problems", Mathematics of Computation, 55 (191): 355–380, Bibcode:1990MaCom..55..355B, doi:10.2307/2008811, JSTOR 2008811
Jaeschke, Gerhard (October 1993), "On strong pseudoprimes to several bases" (PDF), Mathematics of Computation, 61 (204): 915–926, doi:10.2307/2153262, JSTOR 2153262
Jiang, Yupeng; Deng, Yingpu (2014). "Strong pseudoprimes to the first eight prime bases". Mathematics of Computation. 83 (290): 2915–2924. doi:10.1090/S0025-5718-2014-02830-5. S2CID 33599405.
Sorenson, Jonathan; Webster, Jonathan (2015). "Strong Pseudoprimes to Twelve Prime Bases". Mathematics of Computation. 86 (304): 985–1003. arXiv:1509.00864. Bibcode:2015arXiv150900864S. doi:10.1090/mcom/3134. S2CID 6955806.
Zhang, Zhenxiang & Tang, Min (October 2003), "Finding strong pseudoprimes to several bases. II" (PDF), Mathematics of Computation, 72 (44): 2085–2097, Bibcode:2003MaCom..72.2085Z, doi:10.1090/S0025-5718-03-01545-X
Alford, W. R.; Granville, A.; Pomerance, C. (1994), "On the difficulty of finding reliable witnesses", Algorithmic Number Theory (PDF), Lecture Notes in Computer Science, vol. 877, Springer-Verlag, pp. 1–16, doi:10.1007/3-540-58691-1_36, ISBN 978-3-540-58691-3
Robert Baillie; Samuel S. Wagstaff, Jr. (October 1980). "Lucas Pseudoprimes" (PDF). Mathematics of Computation. 35 (152): 1391–1417. doi:10.1090/S0025-5718-1980-0583518-6. MR 0583518.
Burthe Jr., Ronald J. (1996), "Further investigations with the strong probable prime test" (PDF), Mathematics of Computation, 65 (213): 373–381, Bibcode:1996MaCom..65..373B, doi:10.1090/S0025-5718-96-00695-3

free.fr

mpqs.free.fr

Robert Baillie; Samuel S. Wagstaff, Jr. (October 1980). "Lucas Pseudoprimes" (PDF). Mathematics of Computation. 35 (152): 1391–1417. doi:10.1090/S0025-5718-1980-0583518-6. MR 0583518.

harvard.edu

ui.adsabs.harvard.edu

Damgård, I.; Landrock, P. & Pomerance, C. (1993), "Average case error estimates for the strong probable prime test" (PDF), Mathematics of Computation, 61 (203): 177–194, Bibcode:1993MaCom..61..177D, doi:10.2307/2152945, JSTOR 2152945
Bach, Eric (1990), "Explicit bounds for primality testing and related problems", Mathematics of Computation, 55 (191): 355–380, Bibcode:1990MaCom..55..355B, doi:10.2307/2008811, JSTOR 2008811
Sorenson, Jonathan; Webster, Jonathan (2015). "Strong Pseudoprimes to Twelve Prime Bases". Mathematics of Computation. 86 (304): 985–1003. arXiv:1509.00864. Bibcode:2015arXiv150900864S. doi:10.1090/mcom/3134. S2CID 6955806.
Zhang, Zhenxiang & Tang, Min (October 2003), "Finding strong pseudoprimes to several bases. II" (PDF), Mathematics of Computation, 72 (44): 2085–2097, Bibcode:2003MaCom..72.2085Z, doi:10.1090/S0025-5718-03-01545-X
Burthe Jr., Ronald J. (1996), "Further investigations with the strong probable prime test" (PDF), Mathematics of Computation, 65 (213): 373–381, Bibcode:1996MaCom..65..373B, doi:10.1090/S0025-5718-96-00695-3

iacr.org

eprint.iacr.org

Martin R. Albrecht; Jake Massimo; Kenneth G. Paterson; Juraj Somorovsky (15 October 2018). Prime and Prejudice: Primality Testing Under Adversarial Conditions (PDF). ACM SIGSAC Conference on Computer and Communications Security 2018. Toronto: Association for Computing Machinery. pp. 281–298. doi:10.1145/3243734.3243787.

jstor.org

Damgård, I.; Landrock, P. & Pomerance, C. (1993), "Average case error estimates for the strong probable prime test" (PDF), Mathematics of Computation, 61 (203): 177–194, Bibcode:1993MaCom..61..177D, doi:10.2307/2152945, JSTOR 2152945
Bach, Eric (1990), "Explicit bounds for primality testing and related problems", Mathematics of Computation, 55 (191): 355–380, Bibcode:1990MaCom..55..355B, doi:10.2307/2008811, JSTOR 2008811
Jaeschke, Gerhard (October 1993), "On strong pseudoprimes to several bases" (PDF), Mathematics of Computation, 61 (204): 915–926, doi:10.2307/2153262, JSTOR 2153262

miller-rabin.appspot.com

Izykowski, Wojciech. "Deterministic variants of the Miller–Rabin primality test". Retrieved February 24, 2019.

oeis.org

Sloane, N. J. A. (ed.). "Sequence A014233 (Smallest odd number for which Miller–Rabin primality test on bases <= n-th prime does not reveal compositeness)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.

semanticscholar.org

api.semanticscholar.org

Miller, Gary L. (1976), "Riemann's Hypothesis and Tests for Primality", Journal of Computer and System Sciences, 13 (3): 300–317, doi:10.1145/800116.803773, S2CID 10690396
Jiang, Yupeng; Deng, Yingpu (2014). "Strong pseudoprimes to the first eight prime bases". Mathematics of Computation. 83 (290): 2915–2924. doi:10.1090/S0025-5718-2014-02830-5. S2CID 33599405.
Sorenson, Jonathan; Webster, Jonathan (2015). "Strong Pseudoprimes to Twelve Prime Bases". Mathematics of Computation. 86 (304): 985–1003. arXiv:1509.00864. Bibcode:2015arXiv150900864S. doi:10.1090/mcom/3134. S2CID 6955806.

sfu.ca

cecm.sfu.ca

Feitsma, Jan (25 April 2013). Galway, William (ed.). "Tables of pseudoprimes and related data". Centre for Experimental and Constructive Mathematics, Simon Fraser University. Retrieved 2024-11-22.

uniroma2.it

mat.uniroma2.it

Schoof, René (2004), "Four primality testing algorithms" (PDF), Algorithmic Number Theory: Lattices, Number Fields, Curves and Cryptography, Cambridge University Press, ISBN 978-0-521-80854-5

utm.edu

primes.utm.edu

Caldwell, Chris. "Finding primes & proving primality — 2.3: Strong probable-primality and a practical test". The Prime Pages. Retrieved February 24, 2019.