n!!!! + 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
* 345: | \[345!!!!+1\] | 2 × 80923 × 358331 × 141360526676699547157<21> × [59543778474329795201388121516962147269176607396495545546654144171460074193946100005382019926969118931466924027212194321751160890680642098550637269949343<152>] |