A073340 Fibonacci prime pairs: the indices of each pair differ by two and the relevant Fibonacci numbers are both prime.

3, 5, 5, 7, 11, 13, 431, 433, 569, 571

Offset: 1

Author

Harvey P. Dale, Aug 25 2002

Keywords

• more
• nonn

Comments

There are no other Fibonacci prime pairs up to Fibonacci(104911). (See A001605.) Are there any larger terms?

Examples

			The 431st Fibonacci number and the 433rd Fibonacci number are both prime and their indices differ by 2.
		

References

• David Wells, The Penguin Dictionary of Curious and Interesting Numbers, Penguin Books, Rev. ed. 1997, p. 46.

Crossrefs

Cf. A000045, A001605, A279795, A281087.

Programs

Mathematica

Flatten[Select[Partition[Select[Range[3000], PrimeQ[Fibonacci[ # ]]&], 2, 1], #[[2]] - #[[1]] == 2 &]]

Python

from sympy import isprime
def afind(limit):
  i, fnm2, fnm1 = 1, 1, 1
  while i < limit:
    if isprime(fnm2) and isprime(fnm2 + fnm1):
      print(i, i+2, sep=", ", end=", ")
    i, fnm2, fnm1 = i+1, fnm1, fnm2 + fnm1
afind(600) # Michael S. Branicky, Mar 05 2021

Extensions

Offset changed to 1 by Joerg Arndt, Jan 18 2017

a(1) and a(2) prepended by Bobby Jacobs, Jan 18 2017