login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A006945
Smallest odd composite number that requires n Miller-Rabin primality tests.
(Formerly M4673)
3
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.
Same as A014233 except for the first term.
REFERENCES
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).
LINKS
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.
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
Sequence in context: A039917 A376823 A162140 * A089825 A173281 A004820
KEYWORD
nonn,hard,more
AUTHOR
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