n!!!!! - 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
314: | \[314!!!!!-1\] | 5107 × 66617849149457<14> × 4657390685866267<16> × 50814852164615114581793608278116586667390151094041908145681297510619617212340916728621721254678191<98> |