# Prime Fibonacci? Sounds Crazy!

Fibonacci sequence is defined as $$F_0=0 , F_1=1$$ and for $$n \geq 2$$ $F_n=F_{n-1}+F_{n-2}$

So the Fibonacci sequence is $$0,1,1,2,3,5,8,13,...$$

Find the sum of all the terms in the Fibonacci sequence which are less than $$\textbf{1 billion}$$ and are $$\textbf{prime numbers}$$.

Details and assumptions:-

$$\bullet$$ A prime number is the number which has only $$2$$ positive integer divisors, which are $$1$$ and the number itself. No other positive integer divides the number.

$$\bullet$$ 1 is not a prime number, 2 is the only even prime number.

This problem is a part of the set Crazy Fibonacci

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