login
Primes congruent to {0, 2, 3} mod 5.
11

%I #29 Sep 08 2022 08:44:55

%S 2,3,5,7,13,17,23,37,43,47,53,67,73,83,97,103,107,113,127,137,157,163,

%T 167,173,193,197,223,227,233,257,263,277,283,293,307,313,317,337,347,

%U 353,367,373,383,397,433,443,457

%N Primes congruent to {0, 2, 3} mod 5.

%C Also, primes p that are quadratic nonresidues modulo 5 (and from the quadratic reciprocity law, odd p such that 5 is a quadratic nonresidue modulo p). For primes p' that are quadratic residues modulo 5 (and such that 5 is a quadratic residue mod p') see A045468. - _Lekraj Beedassy_, Jul 13 2004

%C Primes p that divide Fibonacci(p+1). - _Ron Knott_, Jun 27 2014

%D G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 3rd ed., Oxford Univ. Press, 1954, Theorem 180

%H Vincenzo Librandi, <a href="/A042993/b042993.txt">Table of n, a(n) for n = 1..1000</a>

%e For prime 7, Fibonacci(8) = 21 = 3*7, for prime 13, Fibonacci(14) = 377 = 13*29.

%t Select[Prime[Range[100]],MemberQ[{0,2,3},Mod[#,5]]&] (* _Harvey P. Dale_, Mar 03 2012 *)

%o (Magma) [p: p in PrimesUpTo(600) | p mod 5 in [0, 2, 3]]; // _Vincenzo Librandi_, Aug 09 2012

%Y Primes dividing A001654.

%Y Cf. A038872 for primes p which divide Fibonacci(p-1). - _Ron Knott_, Jun 27 2014

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_