n!!! - 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
153: | \[153!!!-1\] | 103 × 359 × 951025155319503075232747<24> × 94996009333241765512672973310046219187167218684276048756686221<62> |