A100266 Primes of the form x^16 + y^16.

2, 65537, 4338014017, 2973697798081, 36054040477057, 314707907280257, 184884411482927041, 665698084159890497, 675416609183179841, 2177953490397261761, 8746361693522261761, 18492693803573123777

Offset: 1

Author

T. D. Noe, Nov 11 2004

Keywords

• nonn

Comments

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.

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Generalized Fermat Number.

Crossrefs

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).

Programs

Mathematica

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}]
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 *)
Union[Select[Total[#^16]&/@Tuples[Range[20],2],PrimeQ]] (* Harvey P. Dale, Nov 03 2013 *)