n!!!!! + 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
396: | \[396!!!!!+1\] | 8971 × 1095094811831<13> × 173352565356691787681<21> × 22714641406999232154481733313603582593930600841373326252012424009473234772079544592717779767164367007900437797511307840379541514010175317<137> |