Perrin pseudoprime

Given the Perrin sequenceMathworldPlanetmath, a0=3, a1=0, a2=2 and an=an-3+an-2 for n>2, if n is not prime yet n|an, that number is then called a Perrin pseudoprimeMathworldPlanetmath. The first few Perrin pseudoprimes are 271441, 904631, 16532714, 24658561, 27422714, 27664033, 46672291 (listed in A013998 of Sloane’s OEIS).

By itself this is not a good enough test of primality. Further requiring that an0modn and a-n1modn improves the test but not enough to be preferable to actually factoring out the number. The first few strong Perrin pseudoprimes are 27664033, 46672291, 102690901, 130944133, 517697641 (listed in A018187 of Sloane’s OEIS).

Unlike Perrin pseudoprimes, most other pseudoprimesMathworldPlanetmathPlanetmath ( are because of a congruence relationPlanetmathPlanetmath to a given base.

Title Perrin pseudoprime
Canonical name PerrinPseudoprime
Date of creation 2013-03-22 16:11:33
Last modified on 2013-03-22 16:11:33
Owner CompositeFan (12809)
Last modified by CompositeFan (12809)
Numerical id 5
Author CompositeFan (12809)
Entry type Definition
Classification msc 11B39
Defines strong Perrin pseudoprime