So, 1,1,2,3,5,8,13,21… Any connection to primes?…it appears not. However,

in betweenthe Fibonacci numbers are how much primes? Let’s see:

- 1 and 1: 0
- 1 and 2: 0
- 2 and 3: 0
- 2 and 3: 0
- 5 and 8: 1
- 8 and 13: 1
- 13 and 21: 2
- 21 and 34: 3
- 34 and 55: 5
- 55 and 89: 8
- 89 and 144: 13
Huh. What could this imply? Let me just close with the same annoying (but wonderful) pattern. 1,2,3,5,8,13,21…

**Answer**

Eyebrow raising indeed, though the pattern does not continue as you suggest. I get

0,1,1,2,3,5,7,10,16,23,37,55,84,125,198

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/logn 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.

**Attribution***Source : Link , Question Author : HyperLuminal , Answer Author : Martin Sleziak*