n!!!! + 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
301: | \[301!!!!+1\] | 2 × 16743157 × 3440247858140997161312043279504513291321116333034079061177398373185943269683844003605718104324455706219992909187659546634895335210494977885268709209<148> |