Fibonacci primes

In the Fibonacci series if the nth term is a prime, then n also is prime (except n = 4).

Fibonacci series
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811,...

Primes
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163,...

Examples

• 2 is a prime, it is the 3rd term in the Fibonacci series and 3 is a prime
• 5 is a prime, 5th in the series and 5 is a prime (trivial)
• 13 is a prime, 7th in the series and 7 is a prime
• 89: 11th term
• 233; 13th term
• 1597; 17th term