|
|
A006686
|
|
Octavan primes: primes of the form p = x^8 + y^8.
(Formerly M5428)
|
|
9
|
|
|
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
|
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
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|