n!!!! - 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
* 312: | \[312!!!!-1\] | 3797 × 106307 × [2562639454001423648222600634796182382022185150476985066891991961507998015565075265712772553299492122823811772595614329809236417874229448187526885296422081<154>] |