n!!!! + 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
* 338: | \[338!!!!+1\] | 181 × 823 × 2008186253988647<16> × [86118547607704966471407224801592568106648588580494407136956082621317993302295789306046064427240756947493785106736628205474374862237437533508306694862611684541<158>] |