An important question is: Is an integer prime if and only if it satisﬁes the Perrin condition, n divides xn ? This question was raised by R. Perrin in 1899. A counterexample, now known as a Perrin pseudoprime, was not discovered until 1982: the smallest one is 271441. This is quite remarkable compared to, say, Fermat pseudoprimes with base 2, for which 341 is the smallest example. Recent work by J. Grantham  shows that there are inﬁnitely many Perrin pseudoprimes.It's always gratifying to see one's work referenced, and the letter provides some nice context for my research (better than I did in the paper itself!).
Tuesday, March 22, 2011
Stan Wagon wrote a letter to the editor in the April 2011 Mathematics Magazine about Perrin's sequence and Perrin pseudoprimes. You may not be able to access it on-line (I can't), but it reads in part: