n!!!! - 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
* 267: | \[267!!!!-1\] | 2 × [113117289801619787816519977437603330365248489131480011160705887398629807452216607434407809189500084928133203357907332704100631713867187<135>] |