Prime Fibonacci? Sounds Crazy!

Fibonacci sequence is defined as F0=0,F1=1F_0=0 , F_1=1 and for n2n \geq 2 Fn=Fn1+Fn2F_n=F_{n-1}+F_{n-2}

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

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


Details and assumptions:-

\bullet A prime number is the number which has only 22 positive integer divisors, which are 11 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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