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A014233
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Smallest odd number for which Miller-Rabin primality test on bases <= n-th prime does not reveal compositeness.
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4
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2047, 1373653, 25326001, 3215031751, 2152302898747, 3474749660383, 341550071728321, 341550071728321, 3825123056546413051, 3825123056546413051, 3825123056546413051, 318665857834031151167461, 3317044064679887385961981
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OFFSET
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1,1
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COMMENTS
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Note that some terms are repeated.
Same as A006945 except for first term.
a(12) > 2^64. Hence the primality of numbers < 2^64 can be determined by asserting strong pseudoprimality to all prime bases <= 37 (=prime(12)). Testing to prime bases <=31 does not suffice, as a(11) < 2^64 and a(11) is a strong pseudoprime to all prime bases <= 31 (=prime(11)). - Joerg Arndt, Jul 04 2012
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REFERENCES
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R. Crandall and C. Pomerance, Prime Numbers: A Computational Perspective, Springer, NY, 2001; see p. 157.
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LINKS
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C. Pomerance, J. L. Selfridge and S. S. Wagstaff, Jr., The pseudoprimes to 25.10^9, Mathematics of Computation 35 (1980), pp. 1003-1026.
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FORMULA
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CROSSREFS
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KEYWORD
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nonn,hard,more
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AUTHOR
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EXTENSIONS
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a(12)-a(13) from the Sorenson/Webster reference, Joerg Arndt, Sep 04 2015
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STATUS
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approved
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