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A006686 Octavan primes: primes of the form p = x^8 + y^8.
(Formerly M5428)
8
2, 257, 65537, 2070241, 100006561, 435746497, 815730977, 832507937, 1475795617, 2579667841, 4338014017, 5110698017, 6975822977, 16983628577, 17995718017, 25605764801, 32575757441, 37822859617, 37839636577, 54875880097 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The largest known octavan prime is currently the largest known generalized Fermat prime: The 1353265-digit 145310^262144+1 = (145310^32768)^8+1^8, found by Ricky L Hubbard. - Jens Kruse Andersen, Mar 20 2011

REFERENCES

A. J. C. Cunningham, High quartan factorisations and primes, Messenger of Mathematics, 36, 11 (1907), pp. 145-174.

A. J. C. Cunningham, Binomial Factorisations, Vols. 1-9, Hodgson, London, 1923-1929; see Vol. 1, pp. 245-259.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)

A. J. C. Cunningham, Binomial Factorisations, Vols. 1-9, Hodgson, London, 1923-1929. [Annotated scans of a few pages from Volumes 1 and 2]

EXAMPLE

65537=1^8+4^8

MATHEMATICA

lst={}; Do[If[PrimeQ[a^8+b^8], AppendTo[lst, a^8+b^8]], {a, 100}, {b, a, 100}]; Sort[lst] (T. D. Noe)

Union[Select[Total/@(Tuples[Range[30], 2]^8), PrimeQ]] (* Harvey P. Dale, Apr 06 2013 *)

PROG

(PARI) list(lim)=my(v=List([2]), x8, t); for(x=1, sqrtnint(lim\=1, 8), x8=x^8; forstep(y=1+x%2, min(sqrtnint(lim-x8, 8), x-1), 2, if(isprime(t=x8+y^8), listput(v, t)))); Set(v) \\ Charles R Greathouse IV, Aug 20 2017

CROSSREFS

Intersection of A003380 and A000040. Subsequence of A291206.

Sequence in context: A060890 A294275 A085316 * A100269 A258805 A196288

Adjacent sequences:  A006683 A006684 A006685 * A006687 A006688 A006689

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Corrected and extended by Jud McCranie, Jan 04 2001

STATUS

approved

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Last modified November 12 12:43 EST 2018. Contains 317109 sequences. (Running on oeis4.)