A Specific Magnitude Budget for the Detection of 44 Nuclear Earthquakes near Large Urban Areas subject to a Natural Seismic Hazard was crucial for finding the typical parameters of the Nuclear Earthquakes : $5.9-7.9~M_w$, from 1st January 1960 to 15th September 2023, $R_i <160~km$ with the index $i$ spanning the $1230$ largest cities and having a maximal horizontal shaking ratio $10^{M_w,i} /R_i^2$ for each specific city $i$ satisfying these typical parameters. Therefore, it allows to build a filter $mathcal{F}_Z$ and to filter out a total of $189$ earthquakes around $372$ cities with a relatively low background of Natural Earthquakes with respect to the Nuclear ones. By including the $189$ filtered earthquakes around these $372$ cities, there is a total of $393$ cities having enough seismic data, with respect to a sufficiently large background of the recent smaller earthquakes around these same cities ($M_wgeq M_{w,0} =4.0$, 1980-2022, $R_i < R_{max}=160~km$, Gutenberg-Richter law and $Delta N_i geq 10^{5.9-4.0}>79$ in the case of an absence of filtered earthquakes with the filter $mathcal{F}_Z$), in order to derive the Probability Estimation of having a such maximal horizontal shaking ratio. Finally, there is a 8.4-$sigma$ anomaly from a statistical excess of the maximal horizontal shaking ratio of the filtered earthquakes with the filter $mathcal{F}_Z$ and with a Probability Estimation Cutoff of $<0.43$ (There is an artifact close to $1$ arising from an exponential behavior inside the Probability Estimation formula of having a such maximal horizontal shaking ratio). Of course, by taking some random positions for the $1230$ largest cities, it vanishes completely that 8.4-$sigma$ anomaly.