n!!! - 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
165: | \[165!!!-1\] | 331 × 5130730421789571811<19> × 1304194998309844789524637104561819991888840908255658157659578311401871092179839<79> |