I wasnt able to find any topic on this despite multiple searches. Apologies if this was already covered here.

Can anyone point me in the right direction for further research on the below topic:

I have played recently with the Fibonacci sequence and prime numbers. I have noticed that, at least for certain initial items in that sequence, if you mark all of the primes in the sequence (I did it for numbers: 2(odd prime),3,5,13,89,233,1597,28657) and check their place in the sequence, it also turns out to be a prime. I'm asssuming that 0 is the 0th item. To give some examples: for 2(odd prime) - which is the 3rd number of the sequence - 3 is also a prime, for 13 being 7th number of the sequence - 7 is also prime, for 233 - being 17th number of the sequence - 17 is also a prime. This seems to be true for all primes up to 17 item in the sequence, it then starts to diverge as 19th (19 being a prime) number of the sequence is 4181 which is not a prime.

To give a visual example:

```
    item number Fib number  
    0       0   
    1       1   
    2       1   
prime   3       2   prime   !
not prm 4       3   prime
prime   5       5   prime   !
    6       8   
prime   7       13  prime   !
    8       21  
    9       34  
    10      55  
prime   11      89  prime   !
    12      144 
prime   13      233 prime   !
    14      377 
    15      610 
    16      987 
prime   17      1597    prime   !
    18      2584    
prime   19      4181    not prime
    20      6765    
    21      10946   
    22      17711   
prime   23      28657   prime   !
    24      46368   
    25      75025   
    26      121393  
    27      196418  
    28      317811  
prime   29      514229  prime   !
    30      832040  
prime   31      1346269 not prime
    32      2178309 
    33      3524578 
    34      5702887 
    35      9227465 
    36      14930352    
prime   37      24157817    not prime
    38      39088169    
    39      63245986    
    40      102334155   
    41      165580141

```

Despite there being certain numbers in the sequence which are primes but their sequence order number not being a prime and vice versa, it's still quite interesting to know why is there such a pattern and if it's true for majority of Fibonacci sequence numbers.

Again, apologies if this is something obvious.

TIA for any clarification on this!