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Sep 30, 2013 at 18:39 comment added Emil Jeřábek The bound needs to be a polynomial in $x$. Bonse’s inequality is not quite stated in that way, but taking $p_1,\dots,p_n$ to be all primes below $x$ makes the bound on $p_{n+1}$ something on the order of $e^{x/2}$, which is much too large.
Sep 30, 2013 at 18:32 comment added The Masked Avenger Would Bonse's inequality work? Or does that grow too fast?
Sep 30, 2013 at 17:41 history answered Emil Jeřábek CC BY-SA 3.0