n!!!!! - 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
* 374: | \[374!!!!!-1\] | 173 × 1156716507129307<16> × [1187340968977961954414206337086096324680428193537314046136257172011195108222909205327246157581793802600356034494229938448323939662427423737435393<145>] |