n!!!! + 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
257: | \[257!!!!+1\] | 2 × 191 × 177876136556670870751<21> × 1987720707619949576320089227598670901934819810919455826838842727574894461496222573034728569835273900343393<106> |