n!!! - 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
174: | \[174!!!-1\] | 967 × 3203 × 159361 × 84009764057<11> × 313951153699<12> × 850446608828359826462819568678697761311793407312082620170977224788392713<72> |