n!!!! + 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
253: | \[253!!!!+1\] | 2 × 8612109521<10> × 15318319993<11> × 1991831574181175039303821944584677558914860544487940397480780912256622515419223389601377994446867148123321<106> |