
Glossary: Prime Pages: Top 5000: 
A Lucas prime
is a Lucas number that
is prime. Recall that the Lucas numbers
can be defined as follows:
v_{1} = 1, v_{2} = 3 and v_{n+1} = v_{n} + v_{n1} (n > 2) It can be shown that, for odd m, v_{n} divides v_{nm}. Hence, for v_{n} to be a prime, the subscript n must be a prime, a power of 2, or zero. However, a prime or power of 2 subscript is not sufficient! First of the Lucas primes are v_{n} with n = 0, 2, 4, 5, 7, 8, 11, 13, 16, 17, 19, 31, 37, 41, 47, 53, 61, 71, 79, 113, 313, 353, 503, 613, 617, 863, 1097, 1361, 4787, 4793, 5851, 7741, 8467, 10691, 12251, 13963, 14449, 19469, 35449, 36779, 44507, 51169, 56003, 81671, 89849, 94823, 140057 and 148091.Larger ones will be added to the Top 20's page on Lucas numbers when found. As with the Fibonacci primes and the Mersenne primes, it is conjectured that there are infinitely many Lucas primes. Interestingly, all three types of numbers are generated by simple recurrence relations. This page contributed by T. D. Noe.
See Also: FibonacciNumber References:
Chris K. Caldwell © 19992018 (all rights reserved)
