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 (probable) Pell 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 
(E. W. Weisstein, Mar. 21, 2009). The following table summarizes the
largest known Pell (probable) primes.
 | decimal digits | discoverer | date | status |
 |  | D. Broadhurst and P. Walker | Jul. 2001 | https://t5k.org/primes/page.php?id=24572 |
 |  | probable prime | ||
 |  | probable prime | ||
 |  | probable prime | ||
 |  | probable prime | ||
 |  | probable prime | ||
 |  | T. D. Noe | Sep. 2004 | probable prime |
