A182474 Primes of the form p^q - q, where p and q are primes.

2, 5, 7, 23, 47, 167, 359, 839, 1367, 1847, 2207, 3719, 5039, 7919, 8179, 10607, 11447, 16127, 17159, 19319, 29927, 36479, 44519, 49727, 54287, 57119, 66047, 85847, 97967, 113567, 128879, 177239, 196247, 201599, 218087, 241079, 273527, 292679, 323759, 344567

Offset: 1

Author

Alex Ratushnyak, May 01 2012

Keywords

• nonn
• easy

Examples

			8179 = 2^13 - 13
		

Crossrefs

Cf. A049002 (primes of the form p^2 - 2).

Cf. A057678 (primes of the form 2^p - p).

Programs

Mathematica

nn = 600000; mx = Floor[Log[2, nn]]; t2 = Select[Table[2^n - n, {n, Prime[Range[PrimePi[mx]]]}], PrimeQ]; mx = Floor[Sqrt[nn]]; tp = Select[Table[n^2 - 2, {n, Prime[Range[PrimePi[mx]]]}], PrimeQ]; Union[t2, tp] (* T. D. Noe, May 01 2012 *)
Module[{upto=350000,r},r=Floor[Sqrt[upto+2]];Select[Union[Select[ (#1[[1]]^#1[[2]]-#1[[2]]&)/@Tuples[Prime[Range[r]],2], PrimeQ]], #1<=upto&]] (* Harvey P. Dale, Dec 07 2012 *)

Formula

Union of A049002 and A057678.