n!!!!! - 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
349: | \[349!!!!!-1\] | 52 × 101 × 337 × 414331 × 1409233933649714799661<22> × 16413323675268303426421<23> × 4563868152548114311801488585355070902545614768122978116454190449317963650222832639526731578449<94> |