n!!! - 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
256: | \[256!!!-1\] | 3 × 149 × 75281351 × 2023367146410887203<19> × 1997687042814510842137843<25> × 367233535399838610134827309096333518244410805851064466512264568277291276054348575531539004897048408984622709261674223<117> |