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 prime-valued terms, retaining repeated values and starting at 
, are 2, 3, 2, 5, 5, 7, 17, 29, 277, 367, 853, ...,
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 distinct primes,
in increasing order, are 2, 3, 5, 7, 17, 29, 277, 367, 853, ... (OEIS A074788).
The following table summarizes Perrin probable prime
records reported through 2022.
 | 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 |
 |  | R. Propper | reported Jun. 2022 |
 |  | R. Propper | reported Jun. 2022 |
 |  | R. Propper | reported Jun. 2022 |
(OEIS A112881).
