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A006945 Smallest odd number that requires n Miller-Rabin primality tests.
(Formerly M4673)
9, 2047, 1373653, 25326001, 3215031751, 2152302898747, 3474749660383, 341550071728321, 341550071728321, 3825123056546413051, 3825123056546413051, 3825123056546413051 (list; graph; refs; listen; history; text; internal format)



The tests are performed on sequential prime numbers starting with 2.  Note that some terms are repeated.

Same as A014233 except for the first term.


R. Crandall and C. Pomerance, Prime Numbers: A Computational Perspective, Springer, NY, 2001; see p. 157.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


Table of n, a(n) for n=1..12.

Joerg Arndt, Fxtbook

Eric Bach, Explicit bounds for primality testing and related problems, Mathematics of Computation 55 (1990), pp. 355-380.

G. Jaeschke, On strong pseudoprimes to several bases, Math. Comp., 61 (1993), 915-926.

Yupeng Jiang, Yingpu Deng, Strong pseudoprimes to the first 9 prime bases, arXiv:1207.0063v1 [math.NT], June 30, 2012.

C. Pomerance, J. L. Selfridge and S. S. Wagstaff, Jr., The pseudoprimes to 25.10^9, Mathematics of Computation 35 (1980), pp. 1003-1026.

S. Wagon, Primality testing, Math. Intellig., 8 (No. 3, 1986), 58-61.

Zhenxiang Zhang and Min Tang, Finding strong pseudoprimes to several bases. II, Mathematics of Computation 72 (2003), pp. 2085-2097.

Index entries for sequences related to pseudoprimes


Bach shows that, on the ERH, a(n) >> exp(sqrt(1/2 * x log x)). [Charles R Greathouse IV, May 17, 2011]


Cf. A089105, A089825.

Sequence in context: A232684 A039917 A162140 * A089825 A173281 A004820

Adjacent sequences:  A006942 A006943 A006944 * A006946 A006947 A006948




N. J. A. Sloane.


Extended and description corrected by Jud McCranie Feb 15 1997.

a(10)-a(12) from Charles R Greathouse IV, Aug 14 2010



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Last modified July 24 21:14 EDT 2014. Contains 244897 sequences.