It is not known if there are infinitely many prime Fibonacci numbers. But can one assert that there is no Fibonacci number >2 that is also highly composite (https://en.wikipedia.org/wiki/Highly_composite_number) - or that there are only finitely many such numbers?

**Remarks:** As given in http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibtable.html, every Fibonacci number bigger than 1 [except F(6)=8 and F(12)=144] has at least one prime factor that is *not* a factor of any earlier Fibonacci number. So, Fibonacci numbers tend to have large prime factors and it is quite conceivable that none of them are highly composite. However, a few are seen to be *semiprimes* (https://en.wikipedia.org/wiki/Semiprime). Not sure if the question of whether there are infinitely many Fibonacci semiprimes has been answered.