A173056 Numbers of the form a^b+b^a, a and b are primes.

8, 17, 54, 57, 177, 368, 2169, 2530, 6250, 8361, 94932, 131361, 178478, 524649, 1596520, 1647086, 8389137, 48989176, 129145076, 536871753, 1162268326, 1221074418, 1996813914, 2147484609, 94143190994, 96951758924, 137438954841

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Feb 08 2010

Keywords

• nonn

Comments

2^2+2^2=8, 2^3+3^2=17, 3^3+3^3=54, 2^5+5^2=57, 2^7+7^2=177, 3^5+5^3=368,..

Crossrefs

Cf. A076980, A173054, A173055.

Programs

Mathematica

nMax=10^12; lim=PrimePi[Log[2, nMax]]; f[a_,b_]:=Prime[a]^Prime[b] + Prime[b]^Prime[a]; Select[Union[Flatten[Table[f[a,b], {a,lim}, {b,lim}]]], #<=nMax&]
nMax=10^12; lim=PrimePi[Log[2, nMax]]; Select[Union[First[#]^Last[#] + Last[#]^First[#]&/@ Tuples[Prime[Range[lim]],{2}]], #<=nMax&]  (* Harvey P. Dale, Mar 12 2011 *)