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%I #20 May 21 2022 14:13:58
%S 3,5,5,7,11,13,431,433,569,571
%N Fibonacci prime pairs: the indices of each pair differ by two and the relevant Fibonacci numbers are both prime.
%C There are no other Fibonacci prime pairs up to Fibonacci(104911). (See A001605.) Are there any larger terms?
%D David Wells, The Penguin Dictionary of Curious and Interesting Numbers, Penguin Books, Rev. ed. 1997, p. 46.
%e The 431st Fibonacci number and the 433rd Fibonacci number are both prime and their indices differ by 2.
%t Flatten[Select[Partition[Select[Range[3000], PrimeQ[Fibonacci[ # ]]&], 2, 1], #[[2]] - #[[1]] == 2 &]]
%o (Python)
%o from sympy import isprime
%o def afind(limit):
%o i, fnm2, fnm1 = 1, 1, 1
%o while i < limit:
%o if isprime(fnm2) and isprime(fnm2 + fnm1):
%o print(i, i+2, sep=", ", end=", ")
%o i, fnm2, fnm1 = i+1, fnm1, fnm2 + fnm1
%o afind(600) # _Michael S. Branicky_, Mar 05 2021
%Y Cf. A000045, A001605, A279795, A281087.
%K more,nonn
%O 1,1
%A _Harvey P. Dale_, Aug 25 2002
%E Offset changed to 1 by _Joerg Arndt_, Jan 18 2017
%E a(1) and a(2) prepended by _Bobby Jacobs_, Jan 18 2017