n!!!! - 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
302: | \[302!!!!-1\] | 244597 × 2843397018729003330705175535748429550163020876775783696951940369827661034751836651178716083711613182682655986748410084485630867116464228751783545996067<151> |