n!!! - 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
155: | \[155!!!-1\] | 3 × 1447 × 9925597180027<13> × 1283681274588267907563962809<28> × 1860224749017183352196623386586713700579033233473<49> |