Cockroaches

Trying to get into the refrigerator, cockroach Seryoga could not dodge the fatal slipper of pensioner Agafya Petrovna and died a heroic death. Therefore, on the next dark night, the remaining cockroaches gathered in the kitchen to exact revenge and launch a crusade against the refrigerator. They lined up in a column, with two cockroaches in each row. However, in the last row, there was a spot left for Seryoga. Then, they rearranged into a column with three cockroaches per row, but again, one was missing. Each time, they formed columns with one more cockroach per row than before, and each time, Seryoga was missing. Agafya Petrovna was about to enter the kitchen to prepare breakfast when the cockroaches managed to rearrange themselves $N$ times. What is the minimum number of cockroaches that could live in Agafya Petrovna's apartment?