A100269 Primes of the form x^8 + y^8 with x^4 + y^4, x^2 + y^2 and x+y also prime.

2, 257, 65537, 2724909545357921, 3282116715437377, 40213879071634241, 147578912575757441, 303879829574456257, 697576026529536481, 1316565220482548321, 2860283484326400961, 4080251077774711937

Offset: 1

Author

T. D. Noe, Nov 11 2004

Keywords

• nonn

Comments

The Mathematica program generates numbers of the form x^8 + y^8 in order of increasing magnitude; it accepts a number when all the x^2^k + y^2^k are prime for k=0,1,2,3.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..100
• Eric Weisstein's World of Mathematics, Generalized Fermat Number.

Crossrefs

Cf. A099332, A100268, A100270.

Programs

Mathematica

n=3; 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]]; allPrime=True; k=0; While[k<=n&&allPrime, allPrime=PrimeQ[x^2^k+y^2^k]; k++ ]; !allPrime]; p, {20}]