| Fibonacci Primes
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|---|---|
Basic Info
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| Discovered by | Leonardo Fibonacci |
| Number of | Unknown |
| Description | A prime which is also a term in the Fibonacci sequence |
| First Few | 2, 3, 5, 13, 89, 233, 1597, 28657, 514229, 433494437, 2971215073, 99194853094755497, 1066340417491710595814572169, 19134702400093278081449423917, 475420437734698220747368027166749382927701417016557193662268716376935476241 |
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, for example 1, 1, 2, 3, 5, 8, 13...
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.
