A172142 Primes of form p^q+q^p+1, where p, q are also primes.

2531, 94933, 48989177, 19088056323407827075424486287615602692671561637, 10027860709531471276608129899567499096303854889970269316268113271, 88537996291958256446260440678593208943077817551131498658191653913030830300434060998128240895267

Offset: 1

Author

Cheng Zhang (cz1(AT)rice.edu), Jan 26 2010

Keywords

• nonn

Examples

			a(1) = 3^7+7^3+1 = 2531;
a(2) = 5^7+7^5+1 = 94933;
a(3) = 5^11+11^5+1 = 48989177;
a(4) = 3^97+97^3+1 = 19088056323407827075424486287615602692671561637;
a(5) = 23^47+47^23+1.
		

Crossrefs

Cf. A118097.

Programs

Mathematica

a[n_] := Block[{}, For[l = {}; i = 1, i < n, i++, For[j = i, j < n, j++, p = Prime[i]; q = Prime[j]; x = p^q + q^p + 1; If[PrimeQ[x], l = Append[l, x]]]]; Print[Sort[Union[l]]]]; a[50]
Union[Select[First[#]^Last[#]+Last[#]^First[#]+1&/@Tuples[Prime[Range[50]],2],PrimeQ]] (* Harvey P. Dale, Oct 17 2014 *)