n!!! - 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
154: | \[154!!!-1\] | 32 × 564233 × 4449829213463<13> × 616616817849110788681135511020922921355084714323570481699911552030172809<72> |