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 75479248496430827044831091619765377 81833842440832880856752412600491248324784297704172253450355317535082936750061527 689799541169259849585265122868502865392087298790653950 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.
Title | Poulet number |
---|---|
Canonical name | PouletNumber |
Date of creation | 2013-03-22 18:11:12 |
Last modified on | 2013-03-22 18:11:12 |
Owner | CompositeFan (12809) |
Last modified by | CompositeFan (12809) |
Numerical id | 6 |
Author | CompositeFan (12809) |
Entry type | Definition |
Classification | msc 11A51 |
Synonym | Sarrus number |