A006686 Octavan primes: primes of the form p = x^8 + y^8.

2, 257, 65537, 2070241, 100006561, 435746497, 815730977, 832507937, 1475795617, 2579667841, 4338014017, 5110698017, 6975822977, 16983628577, 17995718017, 25605764801, 32575757441, 37822859617, 37839636577, 54875880097

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

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

Examples

			65537 = 1^8 + 4^8.
		

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]

Crossrefs

Intersection of A003380 and A000040. Subsequence of A291206.

Programs

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 *)

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

Extensions

Corrected and extended by Jud McCranie, Jan 04 2001