%0 Journal Article %T A note on the Polignac numbers %A Hao Pan %J Mathematics %D 2013 %I arXiv %R 10.1017/S0004972713001093 %X Suppose that $k\geq 3.5\times 10^6$ and $\hH=\{h_1,\ldots,h_{k_0}\}$ is admissible. Then for any $m\geq 1$, the set $$ \{m(h_j-h_i):\,h_i