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
KEYWORD
nonn
AUTHOR
EXTENSIONS
Corrected and extended by Jud McCranie, Jan 04 2001
STATUS
approved