This is the Fibonacci Prime!! I had to recreate this 3 times, and each time got faster than the last :D There is an insane amount of caching to make sure the speed is never too slow!
Created for the weekly, it can calculate up to the twelfth number in a reasonable time (between 1-10 minutes). The time increases exponentially I think.
I use caching to make the prime number finder as fast as possible, and basically what happens is we search primes in a pre-determined fibonacci sequence.
Have a great day! Please do tell me how far you got for the fibonacci prime :D