A042993 Primes congruent to {0, 2, 3} mod 5.

2, 3, 5, 7, 13, 17, 23, 37, 43, 47, 53, 67, 73, 83, 97, 103, 107, 113, 127, 137, 157, 163, 167, 173, 193, 197, 223, 227, 233, 257, 263, 277, 283, 293, 307, 313, 317, 337, 347, 353, 367, 373, 383, 397, 433, 443, 457

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

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

Primes p that divide Fibonacci(p+1). - Ron Knott, Jun 27 2014

Examples

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

References

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

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Primes dividing A001654.

Cf. A038872 for primes p which divide Fibonacci(p-1). - Ron Knott, Jun 27 2014

Programs

Magma

[p: p in PrimesUpTo(600) | p mod 5 in [0, 2, 3]]; // Vincenzo Librandi, Aug 09 2012

Mathematica

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