Pell Prime
A Pell prime is a Pell number P_n that is also a prime number. For a Pell number P_n to be prime, it is necessary that n 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 188856 (E. W. Weisstein, Mar. 21, 2009). The following table summarizes the largest known Pell (probable) primes.
n decimal digits discoverer date status
13339 5106 D. Broadhurst and P. Walker Jul. 2001 https://t5k.org/primes/page.php?id=24572
14033 5372 probable prime
23747 9090 probable prime
28183 10788 probable prime
34429 13179 probable prime
36749 14067 probable prime
90197 34525 T. D. Noe Sep. 2004 probable
prime
See also
Integer Sequence Primes, Pell Number, Prime Number, Probable PrimeExplore with Wolfram|Alpha
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References
Ribenboim, P. The New Book of Prime Number Records. New York: Springer-Verlag, pp. 53-57, 1996.Sloane, N. J. A. Sequence A096650 in "The On-Line Encyclopedia of Integer Sequences."Cite this as:
Weisstein, Eric W. "Pell Prime." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PellPrime.html