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%I M4673 #51 Feb 23 2024 07:11:02
%S 9,2047,1373653,25326001,3215031751,2152302898747,3474749660383,
%T 341550071728321,341550071728321,3825123056546413051,
%U 3825123056546413051,3825123056546413051,318665857834031151167461,3317044064679887385961981
%N Smallest odd composite number that requires n Miller-Rabin primality tests.
%C The tests are performed on sequential prime numbers starting with 2. Note that some terms are repeated.
%C Same as A014233 except for the first term.
%D R. Crandall and C. Pomerance, Prime Numbers: A Computational Perspective, Springer, NY, 2001; see p. 157.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Joerg Arndt, <a href="http://www.jjj.de/fxt/#fxtbook">Matters Computational (The Fxtbook)</a>
%H Eric Bach, <a href="https://doi.org/10.1090/S0025-5718-1990-1023756-8">Explicit bounds for primality testing and related problems</a>, Mathematics of Computation 55 (1990), pp. 355-380.
%H G. Jaeschke, <a href="http://dx.doi.org/10.1090/S0025-5718-1993-1192971-8">On strong pseudoprimes to several bases</a>, Math. Comp., 61 (1993), 915-926.
%H Yupeng Jiang, Yingpu Deng, <a href="http://arxiv.org/abs/1207.0063">Strong pseudoprimes to the first 9 prime bases</a>, arXiv:1207.0063v1 [math.NT], June 30, 2012.
%H C. Pomerance, J. L. Selfridge and S. S. Wagstaff, Jr., <a href="http://dx.doi.org/10.1090/S0025-5718-1980-0572872-7">The pseudoprimes to 25.10^9</a>, Mathematics of Computation 35 (1980), pp. 1003-1026.
%H S. Wagon, <a href="http://dx.doi.org/10.1007/BF03025793">Primality testing</a>, Math. Intellig., 8 (No. 3, 1986), 58-61.
%H Zhenxiang Zhang and Min Tang, <a href="http://dx.doi.org/10.1090/S0025-5718-03-01545-X">Finding strong pseudoprimes to several bases. II</a>, Mathematics of Computation 72 (2003), pp. 2085-2097.
%H <a href="/index/Ps#pseudoprimes">Index entries for sequences related to pseudoprimes</a>
%F Bach shows that, on the ERH, a(n) >> exp(sqrt(1/2 * x log x)). [_Charles R Greathouse IV_, May 17 2011]
%e 2047=23*89. 1373653 = 829*1657. 25326001 = 11251*2251. 3215031751 = 151*751*28351. 2152302898747 = 6763*10627*29947.
%Y Cf. A089105, A089825.
%K nonn,hard,more
%O 1,1
%A _N. J. A. Sloane_.
%E Extended and description corrected by _Jud McCranie_ Feb 15 1997.
%E a(10)-a(12) from _Charles R Greathouse IV_, Aug 14 2010
%E a(13)-a(14) copied from A014233 by _Max Alekseyev_, Feb 15 2017
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