It was proved by Rankin in 1963 that there are infinitely many $n$ for which $$j(n) \geq (C+o(1) \frac{\log(n) \log_{2}(n) \log_{4}(n)}{\log^{2}_{3}(n)} $$ holds for some positive $C>0$. The value of $C$ has since been improved by Maier and Pomerance (1990) to $C=1.3125...$ and Pintz (1997) to $C=2e^{\gamma}$ (where $\gamma$ is Euler's constant).

It was proved by Rankin in 1963 that there are infinitely many $n$ for which $$j(n) \geq (C+o(1) \frac{\log(n) \log_{2}(n) \log_{4}(n)}{\log^{2}_{3}(n)} $$ holds for some positive $C>0$. The value of $C$ has since been improved by Maier and Pomerance (1990) to $C=e^{\gamma} \times 1.3125...$ and Pintz (1997) to $C=2e^{\gamma}$ (where $\gamma$ is Euler's constant).

It was proved by Rankin in 1963 that $$j(n) \geq (C+o(1) \frac{\log(x) \log_{2}(n) \log_{4}(n)}{\log^{2}_{3}(n)} $$ holds for some positive $C>0$. The value of $C$ has since been improved by Maier and Pomerance (1990) to $C=1.3125...$ and Pintz (1997) to $C=2e^{\gamma}$ (where $\gamma$ is Euler's constant).

It was proved by Rankin in 1963 that there are infinitely many $n$ for which $$j(n) \geq (C+o(1) \frac{\log(n) \log_{2}(n) \log_{4}(n)}{\log^{2}_{3}(n)} $$ holds for some positive $C>0$. The value of $C$ has since been improved by Maier and Pomerance (1990) to $C=1.3125...$ and Pintz (1997) to $C=2e^{\gamma}$ (where $\gamma$ is Euler's constant).