n!!!! - 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
* 313: | \[313!!!!-1\] | 22 × 131 × 12841 × 147852330094679803<18> × [3415870742901167202110192214350675563838288658453039061532706185607030273557678824228371691431040844931386447116591766984412455954362220437<139>] |