Note: These queries had come up during an earlier discussion: On Fibonacci numbers that are also highly composite. Am putting them up as a separate post.

1. Are there any Fibonacci numbers that are sandwiched between twin primes? An observation: none of the first 30 odd Fibonacci numbers is sandwiched between twin primes.

2. There are instances of "highly composites between twin primes" such as 60 which falls between twin primes 59 and 61 and 180 which is between 179 and 181. Can an upper bound be established for such highly composite numbers?

Note: These queries had come up during an earlier discussion: On Fibonacci numbers that are also highly composite. Am putting them up as a separate post.

Q: Are there any Fibonacci numbers that are sandwiched between twin primes? An observation: none of the first 30 odd Fibonacci numbers is sandwiched between twin primes.