Poulet number
A Poulet number or Sarrus number is a composite integer such that . In other words, a base 2 pseudoprime
(thus a Poulet number that satisfies the congruence
for other bases is a Carmichael number). The first few Poulet numbers are 341, 561, 645, 1105, 1387, 1729, 1905, listed in A001567 of Sloane’s OEIS.
For example, 561 is a Poulet number, since is 7547924849643082704483109161976537781833842440832880856752412600491248324784297704172253450355317535082936750061527689799541169259849585265122868502865392087298790653950 and that’s divisible by 561. The number 561 is not prime, it has the prime factors 3, 11, and 17.
Poulet numbers are counterexamples to the Chinese hypothesis.
References
- 1 Derrick Henry Lehmer, “Errata for Poulet’s table,” Math. Comp. 25 25 (1971): 944 - 945.