Fermat Pseudoprime

A Fermat pseudoprime to a base , written psp(), is a Composite Number such that (i.e.,it satisfies Fermat's Little Theorem, sometimes with the requirement that must be Odd; Pomerance et al. 1980). psp(2)s are called Poulet Numbers or, less commonly, Sarrus Numbers orFermatians (Shanks 1993). The first few Even psp(2)s (including the Prime 2 as a pseudoprime)are 2, 161038, 215326, ... (Sloane's A006935).

If base 3 is used in addition to base 2 to weed out potential Composite Numbers, only 4709Composite Numbers remain . Adding base 5 leaves 2552, and base 7 leaves only1770 Composite Numbers.

References

Pomerance, C.; Selfridge, J. L.; and Wagstaff, S. S. ``The Pseudoprimes to .'' Math. Comput. 35, 1003-1026, 1980. Available electronically from ftp://sable.ox.ac.uk/pub/math/primes/ps2.Z.

Shanks, D. Solved and Unsolved Problems in Number Theory, 4th ed. New York: Chelsea, p. 115, 1993.

Sloane, N. J. A. SequenceA006935/M2190in ``An On-Line Version of the Encyclopedia of Integer Sequences.''http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.

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