A006945 Smallest odd composite number that requires n Miller-Rabin primality tests. (Formerly M4673)

9, 2047, 1373653, 25326001, 3215031751, 2152302898747, 3474749660383, 341550071728321, 341550071728321, 3825123056546413051, 3825123056546413051, 3825123056546413051, 318665857834031151167461, 3317044064679887385961981

Offset

1,1

Comments

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

References

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

Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004. See p. 98.

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

Links

Table of n, a(n) for n=1..14.

Joerg Arndt, Matters Computational (The 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.

J. Sorenson and J. Webster, Strong pseudoprimes to twelve prime bases, Math. Comput. 86 (2017) no 304, 985-1003.

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

Formula

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

Example

2047=23*89. 1373653 = 829*1657. 25326001 = 11251*2251. 3215031751 = 151*751*28351. 2152302898747 = 6763*10627*29947.

Crossrefs

Same as A014233 except for the first term.

Cf. A089105, A089825.

Sequence in context: A039917 A376823 A162140 * A089825 A173281 A004820

Adjacent sequences: A006942 A006943 A006944 * A006946 A006947 A006948

Keyword

nonn,hard,more

Author

N. J. A. Sloane

Extensions

Extended and description corrected by Jud McCranie Feb 15 1997.

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

a(13)-a(14) copied from A014233 by Max Alekseyev, Feb 15 2017

Status

approved