Fibonacci prime
| No. of known terms | 49 |
|---|---|
| Conjectured no. of terms | Infinite |
| First terms | 2, 3, 5, 13, 89, 233 |
| Largest known term | F2904353 |
| OEIS index | A001605 |
A Fibonacci prime is a Fibonacci number that is prime, a type of integer sequence prime.
The first Fibonacci primes are (sequence in the OEIS):
It is not known whether there are infinitely many Fibonacci primes. With the indexing starting with F1 = F2 = 1, the first 33 are Fn for the n values (sequence in the OEIS):
In addition to these proven Fibonacci primes, there have been found probable primes for
Except for the case n = 4, all Fibonacci primes have a prime index, because if a divides b, then also divides , but not every prime is the index of a Fibonacci prime.
Fp is prime for 8 of the first 10 primes p; the exceptions are F2 = 1 and F19 = 4181 = 37 × 113. However, Fibonacci primes become rarer as the index increases. Fp is prime for only 26 of the 1,229 primes p below 10,000. The number of prime factors in the Fibonacci numbers with prime index are:
...
Wikipedia