from (f) we have:
x/p_{j+1} + x/p_{j+2} + ...\ge x-N_j(x),
form (d) we have:
N_j (x)< x/2.
So:
x/p_{j+1} + x/p_{j+2} + ...\ge x-N_j(x)>x-x/2=x/2
Now divide through by x:
1/p_{j+1} + 1/p_{j+2} + ...>1/2,
which from (e) we know means that:
1/1 + 1/3 + ..+ 1/p_n + ...
diverges.
(sorry but LaTeX seems to be not working again!!) I think I have sorted out the LaTeX now, but will leave this here just in case.
RonL