## Fibonacci Conjecture

### January 23, 2015

The sequence of Fibonacci numbers is defined as *F*_{0} = 0, *F*_{1} = 1, *F*_{n} = *F*_{n−2} + *F*_{n−1}. It has been conjectured that for any Fibonacci number *F*, *F*^{2} + 41 is composite.

Your task is to either prove the conjecture to be true or find a counter-example that demonstrates it is false (hint: this is not a blog about proving math theorems). When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

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Quick and dirty brute-force method in python. Copy and pasted the isprime function, made a fibb generator, and started testing for anomalies.

Detected 2^2 + 41 as the odd one out:

NEVER MIND, IGNORE MY PREVIOUS COMMENT, NOT THE SOLUTION.

I am truly a poop.

Fails for F_0, as 41 is prime.

I think that according to the definition in the question the value of n in the model solution is off by 2.

For that definition, the initialisation line would be

i took 1 as first fibonacci number and run my code in several ranges as my machine lets me.

it seems conjecture is true. though if it is not, i will not be surprised.

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