n!!! - 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
* 317: | \[317!!!-1\] | 3 × 690817931 × 4583637944459154289<19> × [706700379514454516569441763265282210575754322288397131737639246006027618244330522338775696725512664627537585804784680575383307517939593789190598341899820432710122838802790895047472486306351887<192>] |