A Perrin prime is a Perrin sequence number 
that is also a prime
number. Note this is distinct from a Perrin
pseudoprime, which is a composite number 
satisfying the divisibility condition
.
The first few Perrin primes are 2, 3, 2, 5, 5, 7, 17, 29, 277, 367, 853, ... (OEIS A074788), which occur for terms 
, 3, 4, 5, 6, 7, 10, 12, 20, 21, 24, 34, 38, 75, 122, 166,
236, 355, 356, 930, 1042, 1214, 1461, 1622, 4430, 5802, 9092, 16260, 18926, 23698,
40059, 45003, 73807, 91405, 263226, 316872, 321874, 324098, ... (OEIS A112881),
the largest of which are probable primes. The following
table summarizes the largest known Perrin (probable) primes.
 | decimal digits | discoverer | date |
 |  | E. W. Weisstein | Oct. 6, 2005 |
 |  | E. W. Weisstein | May 4, 2006 |
 |  | E. W. Weisstein | Feb. 4, 2007 |
 |  | E. W. Weisstein | Feb. 19, 2007 |
 |  | E. W. Weisstein | Feb. 25, 2007 |
 |  | E. W. Weisstein | Feb. 15, 2011 |
