# Eyebrow-raising pattern of number of primes between terms of the Fibonacci number sequence?

So, $$1,1,2,3,5,8,13,21…1,1,2,3,5,8,13,21...$$ Any connection to primes?…it appears not. However, in between the Fibonacci numbers are how much primes? Let’s see:

• $$11$$ and $$11$$: $$00$$
• $$11$$ and $$22$$: $$00$$
• $$22$$ and $$33$$: $$00$$
• $$22$$ and $$33$$: $$00$$
• $$55$$ and $$88$$: $$11$$
• $$88$$ and $$1313$$: $$11$$
• $$1313$$ and $$2121$$: $$22$$
• $$2121$$ and $$3434$$: $$33$$
• $$3434$$ and $$5555$$: $$55$$
• $$5555$$ and $$8989$$: $$88$$
• $$8989$$ and $$144144$$: $$1313$$

Huh. What could this imply? Let me just close with the same annoying (but wonderful) pattern. $$1,2,3,5,8,13,21…1,2,3,5,8,13,21...$$

Remember that the the number of primes has a well known growth rate (https://en.wikipedia.org/wiki/Prime_number_theorem). Since the Fibonacci numbers are relatively spread out, using $n/\log n$ to approximate the number of primes less than $n$ will cause the number of primes between them to behave like the growth rate of the primes.