A173907 Primes of form x^y+y^x where x and y are composite numbers.

43143988327398957279342419750374600193, 5052785737795758503064406447721934417290878968063369478337, 205688069665150755269371147819668813122841983204711281293004769, 3329896365316142756322307042065269797678257903507506764421250291562312417, 814539297859635326656252304265822609649892589675472598580095801187688932052096060144958129

Offset: 1

Author

Juri-Stepan Gerasimov, Mar 02 2010

Keywords

• nonn

Examples

			The first 5 terms are 15^32+32^15, 33^38+38^33, 8^69+69^8, 9^76+76^9, 21^68+68^21.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..33 (all terms < 10^999)
• Robert Israel, Representations of the first 46 terms as x^y + y^x

Crossrefs

Cf. A061119, A094133, A162488, A162490, A045344.

Programs

Maple

N:= 10^100: # for terms <= N
R:= NULL:
for x from 4 while 2*x^x < N do
  if isprime(x) then next fi;
  for y from x+1 do
    if igcd(x,y) > 1 or isprime(y) then next fi;
    q:= x^y + y^x;
    if q > N then break fi;
    if isprime(q) then R:= R,q  fi;
od od:
sort([R]); # Robert Israel, Jul 11 2025

Extensions

a(3)-a(5) from Franklin T. Adams-Watters, Mar 22 2010

Definition corrected by N. J. A. Sloane, Apr 13 2010