cp's OEIS Frontend

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

%I A173907 #14 Jul 16 2025 01:15:19
%S A173907 43143988327398957279342419750374600193,
%T A173907 5052785737795758503064406447721934417290878968063369478337,
%U A173907 205688069665150755269371147819668813122841983204711281293004769,3329896365316142756322307042065269797678257903507506764421250291562312417,814539297859635326656252304265822609649892589675472598580095801187688932052096060144958129
%N A173907 Primes of form x^y+y^x where x and y are composite numbers.
%H A173907 Robert Israel, <a href="/A173907/b173907.txt">Table of n, a(n) for n = 1..33</a> (all terms < 10^999)
%H A173907 Robert Israel, <a href="/A173907/a173907.txt">Representations of the first 46 terms as x^y + y^x</a>
%e A173907 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.
%p A173907 N:= 10^100: # for terms <= N
%p A173907 R:= NULL:
%p A173907 for x from 4 while 2*x^x < N do
%p A173907   if isprime(x) then next fi;
%p A173907   for y from x+1 do
%p A173907     if igcd(x,y) > 1 or isprime(y) then next fi;
%p A173907     q:= x^y + y^x;
%p A173907     if q > N then break fi;
%p A173907     if isprime(q) then R:= R,q  fi;
%p A173907 od od:
%p A173907 sort([R]); # _Robert Israel_, Jul 11 2025
%Y A173907 Cf. A061119, A094133, A162488, A162490, A045344.
%K A173907 nonn
%O A173907 1,1
%A A173907 _Juri-Stepan Gerasimov_, Mar 02 2010
%E A173907 a(3)-a(5) from _Franklin T. Adams-Watters_, Mar 22 2010
%E A173907 Definition corrected by _N. J. A. Sloane_, Apr 13 2010