Fibonacci number in product of prime form

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How do you find the primes factor of fibonacci number? I knew that every Fibonacci number bigger than 1 [except F(6)=8 and F(12)=144] has at least one prime factor that is not a factor of any earlier Fibonacci number.

For example $F_{19} = 37 * 113$

37 and 113 are prime but how do you find this pair of prime product of fibonacci number?