n!!!! - 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
222: | \[222!!!!-1\] | 131 × 1230766157 × 1722435892434718305225814689757126152986608378147207380812686853054782760181706205289341672029097<97> |