n!!!! - 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
256: | \[256!!!!-1\] | 43177385615549271523898157221679103532856783609871956187460970541314103038150206562235255909033916874351844943462399999999999999<128> |