%I M5428 #35 Dec 26 2021 21:50:25
%S 2,257,65537,2070241,100006561,435746497,815730977,832507937,
%T 1475795617,2579667841,4338014017,5110698017,6975822977,16983628577,
%U 17995718017,25605764801,32575757441,37822859617,37839636577,54875880097
%N Octavan primes: primes of the form p = x^8 + y^8.
%C 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
%D A. J. C. Cunningham, High quartan factorisations and primes, Messenger of Mathematics, 36, 11 (1907), pp. 145-174.
%D A. J. C. Cunningham, Binomial Factorisations, Vols. 1-9, Hodgson, London, 1923-1929; see Vol. 1, pp. 245-259.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Charles R Greathouse IV, <a href="/A006686/b006686.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from T. D. Noe)
%H A. J. C. Cunningham, <a href="/A001912/a001912.pdf">Binomial Factorisations</a>, Vols. 1-9, Hodgson, London, 1923-1929. [Annotated scans of a few pages from Volumes 1 and 2]
%e 65537 = 1^8 + 4^8.
%t lst={}; Do[If[PrimeQ[a^8+b^8], AppendTo[lst, a^8+b^8]], {a, 100}, {b, a, 100}]; Sort[lst] (T. D. Noe)
%t Union[Select[Total/@(Tuples[Range[30],2]^8),PrimeQ]] (* _Harvey P. Dale_, Apr 06 2013 *)
%o (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
%Y Intersection of A003380 and A000040. Subsequence of A291206.
%K nonn
%O 1,1
%A _N. J. A. Sloane_
%E Corrected and extended by _Jud McCranie_, Jan 04 2001