Factoring integers defined by second and third order recurrence relations

Factoring the first two-hundred and fifty Fibonacci numbers using just trial division would take an unreasonable amount of time. Instead the problem must be attacked using modern factorization algorithms. We look not only at the Fibonacci numbers, but also at factoring integers defined by other second and third order recurrence relations. Specifically we include the Fibonacci, Tribonacci and Lucas numbers. We have verified the known factorizations of first 382 Fibonacci numbers and the first 185 Lucas numbers, we also completely factored the first 311 Tribonacci numbers