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%I #17 Feb 21 2023 06:18:22
%S 2,65537,4338014017,2973697798081,36054040477057,314707907280257,
%T 184884411482927041,665698084159890497,675416609183179841,
%U 2177953490397261761,8746361693522261761,18492693803573123777
%N Primes of the form x^16 + y^16.
%C The Mathematica program generates numbers of the form x^16 + y^16 in order of increasing magnitude; it accepts a number when it is prime.
%H T. D. Noe, <a href="/A100266/b100266.txt">Table of n, a(n) for n = 1..1000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GeneralizedFermatNumber.html">Generalized Fermat Number</a>.
%t n=4; pwr=2^n; xmax=2; r=Range[xmax]; num=r^pwr+r^pwr; Table[While[p=Min[num]; x=Position[num, p][[1, 1]]; y=r[[x]]; r[[x]]++; num[[x]]=x^pwr+r[[x]]^pwr; If[x==xmax, xmax++; AppendTo[r, xmax+1]; AppendTo[num, xmax^pwr+(xmax+1)^pwr]]; !PrimeQ[p]]; p, {15}]
%t q=16;lst={};Do[Do[p=n^q+m^q;If[PrimeQ[p],AppendTo[lst,p]],{n,0,5!}],{m,0,5!}];lst;Length[lst];Take[Union[lst],55] (* _Vladimir Joseph Stephan Orlovsky_, Feb 21 2009 *)
%t Union[Select[Total[#^16]&/@Tuples[Range[20],2],PrimeQ]] (* _Harvey P. Dale_, Nov 03 2013 *)
%Y Cf. A100267 (primes of the form x^32 + y^32), A006686 (primes of the form x^8 + y^8), A002645 (primes of the form x^4 + y^4), A002313 (primes of the form x^2 + y^2).
%K nonn
%O 1,1
%A _T. D. Noe_, Nov 11 2004
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