Module[{prod=2, nx, ls={2}}, Do[nx=NextPrime[prod]; prod=prod*nx; AppendTo[ ls, nx], {10}]; ls] (*
Harvey P. Dale, Jul 07 2013 *)
nxt[{p_, a_}]:=Module[{c=NextPrime[p]}, {p*c, c}]; NestList[nxt, {2, 2}, 10][[All, 2]] (*
Harvey P. Dale, Jun 10 2020 *)
