n!!!! + 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
238: | \[238!!!!+1\] | 499349 × 6170653 × 46509443 × 2035209503 × 107056675299788488093<21> × 31939385310968044303764704681<29> × 806107798025359042766063466676737409969<39> |