Fibonacci prime

The Fibonacci prime (English Fibonacci prime ) is the subject of number theory. Is a natural number which has the capacity to be both Fibonacci number and a prime number.

Examples of Fibonacci primes

The sequence of Fibonacci primes begins with the following ten numbers (see sequence A005478 in OEIS ):

In the literature to date, the largest known Fibonacci primes

Mentioned.

It is extremely large numbers. The Fibonacci prime example is a number with decimal digits.

Primality testing

There are a number of conditions to which you may incur for the primality test of Fibonacci numbers and their divisibility.

One of these conditions is the following:

This leads to the following important condition:

This condition is necessary but not sufficient. This takes you to the fact that one finds many Fibonacci numbers whose index is prime and which are yet no Fibonacci primes. The three smallest sample cases for this are:

Unsolved problem

As one of the great unsolved problem related to the Fibonacci primes applies the question:

The Israeli astrophysicist and science writer Mario Livio writes:

The solution of the problem is considered of the British mathematician Richard K. Guy 's view as highly unlikely, he writes: