sylvainjulien dans Non classé 20 août 201520 août 2015 76 Words

Proof that eta(n)>2: case n multiple of 3

Suppose $n>26$ is a multiple of $3$ . One can assume without loss of generality that $r_{0}(n)>2$ . Hence $2r_{0}(n)$ is a Goldbach gap greater than $5$ and thus there are at least three different Goldbach gaps, namely $2$ , $4$ and $2r_{0}(n)$ , hence $\eta(n)>2$ .