I have read that we do not know if there are an infinite number of Fibonacci primes. So far, no one has produced a proof to show if they are infinite. I wanted to know why this seems to be so challenging? I'm sure it is, and maybe there is a subtle mathematical principle I am missing. I thought of using Cantor's set theory. I essentially would compare the set of Fibonacci primes with the natural numbers and since both have cardinality aleph null, that should imply that the Fibonacci primes are infinite. Right? If anyone has any insight into this open problem, please let me know. I would be very interested in your input.