n!!! - 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
342: | \[342!!!-1\] | 269 × 279557 × 13632830897756423<17> × 6115842324837695228800625287419511536383871530555167483978048151662022437579901228743959878508577058046155200359564904712239846097887988581130618928531222530901686915257961881494968475930758144104463485671665461245961<217> |