OFFSET
1,1
COMMENTS
Conjecture (A. Granville, H. te Riele and J. van de Lune, 1989) Let, for even N, p=p(N) be the least prime such that N-p is prime as well. Then p(N)=O((log(N))^2log(log(N))). [Vladimir Shevelev, Dec 08 2008]
It is conjectured that a(n) >= prime(k+1) + 3. See Conjecture C p. 2 in Phong & Dongdong. - Michel Marcus, Aug 02 2017
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..1000
Andrew Granville, J. Van de Lune, and Herman te Riele, Checking the Goldbach Conjecture on a vector computer, Number Theory and Applications (1989), pp. 423-434.
Bui Minh Phong, Li Dongdong, Elementary problems which are equivalent to the Goldbach’s conjecture, Acta Academiae Paedagogicae Agriensis, Sectio Mathematicae 31 (2004) 33-37.
MATHEMATICA
Bag={};
f[n_]:=NestList[NextPrime, 2, n];
GoldbachTest[n_?EvenQ, p_List]:=Block[{m=Length[p], i=1}, While[i<=m&&CompositeQ[n-p[[i]]], i+=1]; If[i>m, {0, 0}, {#, n-#}&[p[[i]]]]];
Do[n=4; While[(GoldbachTest[n, f[j]])!={0, 0}, {n=n+2}]; AppendTo[Bag, n], {j, 0, 44}]; Bag (* Gilmar Rodriguez Pierluissi, Aug 23 2018 *)
PROG
(PARI) a(n)=my(P=prime(n)); forstep(k=6, 9e99, 2, forprime(p=3, P, if(isprime(k-p), next(2))); return(k)) \\ Charles R Greathouse IV, Sep 04 2011
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, Dec 06 2008
STATUS
approved