n!!!! - 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
307: | \[307!!!!-1\] | 2 × 353 × 9590257 × 164031001 × 6367310839<10> × 754282279905742379411325677<27> × 134047470004897128132952911865735569449<39> × 1275825400132208011833672821351669060296724469477761416117163983751<67> |