There is one proof about infinitude of prime with following method,
http://www.ams.org/mathscinet-getitem?mr=2271540
Also it is well know that any two consecutive Fibonacci numbers are mutually prime.
My question, can the proof be used for proving there are infinitely many primes in Fibonacci sequence?
Best Answer
No. If you apply that method to the Fibonacci numbers you get (at best) that there are infinitely many primes dividing Fibonacci numbers. This doesn't imply that there are infinitely many Fibonacci primes.