A100267 Primes of the form x^32 + y^32.

2, 3512911982806776822251393039617, 2211377674535255285545615254209921, 476961452964007550415682034114910337, 14748002492224459115975467901357427939457

Offset: 1

Author

T. D. Noe, Nov 11 2004

Keywords

• nonn

Comments

The Mathematica program generates numbers of the form x^32 + y^32 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. A100266 (primes of the form x^16 + y^16), 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=5; 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, {10}]