Fibonacci Primes

Fibonacci Primes are prime numbers that are also of the Fibonacci Sequence. The Fibonacci Sequence is formed by adding the two preceding numbers to form a third. The first two terms are 1.

In the Fibonacci series, any number which appears as a position n is the sequence divides the number at position 2n, 3n, 4n, etc. in the sequence. For example, the fourth Fibonacci number, F4 = 3, divides F8 (21), F12 (144) and F16 (987), and all further Fibonacci numbers at a position that is a multiple of 4. As a result, a Fibonacci Prime can only appear at a prime valued position in the Fibonacci series, with the exception of F4 = 3 (which is a multiple of F2 = 1). The converse is not true, however, as the 19th Fibonacci number (4181), for example, is a composite number.

The First Few Fibonacci Primes
2

3

5

13

89

233