A080327 Numbers k for which Lucas(k) and Fibonacci(k) are both prime.

4, 5, 7, 11, 13, 17, 47, 148091

Offset: 1

Author

T. D. Noe, Feb 15 2003

Keywords

• hard
• nonn
• more

Comments

The intersection of A001605 and A001606. Fibonacci(148091) and Lucas(148091) are probable primes.

Corresponding Fibonacci-Lucas prime twins are listed in A121533. Corresponding Lucas-Fibonacci prime twins are listed in A121534. Fibonacci(148091) and Lucas(148091) are probable Fibonacci-Lucas and Lucas-Fibonacci prime twins. They have 30949 and 30950 digits. - Alexander Adamchuk, Aug 05 2006

Heuristically, this sequence is finite. It is quite probable, but presently unprovable, that it is now complete. - David Broadhurst, Jun 25 2008

Western Number Theory problem 007:13 by Gary Walsh asks to prove that a(8) = 148091 is in this sequence. - Charles R Greathouse IV, May 21 2014

References

• Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004. See p. 246.

Links

• David Broadhurst, Prime Curio: 10660...49391 (61899-digits)
• Gerry Myerson, Western Number Theory Problems, 17 & 19 Dec 2007.

Crossrefs

Cf. A001605, A001606, A121533, A121534, A000045, A005478, A000032, A000204, A005479, A080327.

Programs

Mathematica

Select[Range[0, 100], PrimeQ[Fibonacci[#]] && PrimeQ[LucasL[#]] & ] (* Robert Price, May 27 2019 *)

PARI

is(n)=isprime(n) && ispseudoprime(fibonacci(n)) && ispseudoprime(fibonacci(n-1)+fibonacci(n+1)) \\ Charles R Greathouse IV, May 21 2014