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Search: id:A100269
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| A100269 |
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Primes of the form x^8 + y^8 with x^4 + y^4, x^2 + y^2, and x+y also prime. |
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3
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| 2, 257, 65537, 2724909545357921, 3282116715437377, 40213879071634241, 147578912575757441, 303879829574456257, 697576026529536481, 1316565220482548321, 2860283484326400961, 4080251077774711937
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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.
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LINKS
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Eric Weisstein's World of Mathematics, Generalized Fermat Number
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MATHEMATICA
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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}]
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CROSSREFS
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Cf. A099332, A100268, A100270.
Sequence in context: A060890 A085316 A006686 this_sequence A128697 A089663 A103029
Adjacent sequences: A100266 A100267 A100268 this_sequence A100270 A100271 A100272
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KEYWORD
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nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Nov 11 2004
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