n!!!! + 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
316: | \[316!!!!+1\] | 74727509647833476266959589<26> × 4374178897977919816548784507166596324262663863595349669244893199036808882587901441926389081846430026764209913328500295806786543160652483309<139> |