An industrial fermentor containing $10,000\:L$ of medium needs to be sterilized. The initial spore concentration in the medium is $10^{6}$ spores $mL^{-1}$. The desired probability of contamination after sterilization is $10^{-3}$. The death rate of spores at $121 \:^{\circ}C$ is $4$ min$^{-1}$. Assume that there is no cell death during heating and cooling phases. The holding time of the sterilization process is___________ min (rounded off to the nearest integer).
