A Pell prime is a Pell number 
that is also a prime number.
For a Pell number 
to be prime, it is necessary
that 
be prime.
The indices of Pell primes and probable primes are 2, 3, 5, 11, 13, 29, 41, 53, 59, 89, 97, 101, 167, 181, 191, 523, 929, 1217,
1301, 1361, 2087, 2273, 2393, 8093, 13339, 14033, 23747, 28183, 34429, 36749, 90197,
... (OEIS A096650), with no others less than
reported in a search by E. W. Weisstein
(pers. comm., Mar. 21, 2009). The following table summarizes large Pell probable
primes known at that time.
 | decimal digits | discoverer | date | status |
 |  | D. Broadhurst and P. Walker | Jul. 2001 | probable prime |
 |  | probable prime | ||
 |  | probable prime | ||
 |  | probable prime | ||
 |  | probable prime | ||
 |  | probable prime | ||
 |  | T. D. Noe | Sep. 2004 | probable prime |
E. W. Weisstein reported no additional examples in a search to index 277096 on Oct. 9, 2015.
