A Poulet number is a Fermat pseudoprime to base 2, denoted psp(2), i.e., a composite number 
such that
The first few Poulet numbers are 341, 561, 645, 1105, 1387, ... (OEIS A001567).
Pomerance et al. (1980) computed all 
Poulet numbers less than 
. The numbers less than 
, 
, ..., are 0, 3, 22, 78, 245, ... (OEIS A055550).
Pomerance has shown that the number of Poulet numbers less than 
for sufficiently large 
satisfy
![exp[(lnx)^(5/14)]<P_2(x)<xexp(-(lnxlnlnlnx)/(2lnlnx))](https://txtdot.deep-swarm.xyz/proxy/img?url=https%3A%2F%2Fmathworld.wolfram.com%2Fimages%2Fequations%2FPouletNumber%2FNumberedEquation2.svg){kind=small}
(Guy 1994).
A Poulet number all of whose divisors 
satisfy 
is called a super-Poulet
number. There are an infinite number of Poulet numbers which are not super-Poulet
numbers. Shanks (1993) calls any integer satisfying 
(i.e., not limited to odd
composite numbers) a Fermatian.
See also
Fermat Pseudoprime, Pseudoprime, Rotkiewicz Theorem, Super-Poulet Number
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References
Guy, R. K. Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 28-29,
1994.Pinch, R. G. E. "The Pseudoprimes Up to 
." ftp://ftp.dpmms.cam.ac.uk/pub/PSP/.Pomerance,
C.; Selfridge, J. L.; and Wagstaff, S. S. Jr. "The Pseudoprimes to
." Math. Comput. 35,
1003-1026, 1980. http://mpqs.free.fr/ThePseudoprimesTo25e9.pdf.Shanks,
D. Solved
and Unsolved Problems in Number Theory, 4th ed. New York: Chelsea, pp. 115-117,
1993.Sloane, N. J. A. Sequences A001567/M5441
and A055550 in "The On-Line Encyclopedia
of Integer Sequences."
Referenced on Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Poulet Number." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PouletNumber.html