n!!!!! + 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
| 311: | \[311!!!!!+1\] | 317 × 19501 × 2001555823104772013<19> × 10599848696013874568985009001647911<35> × 12961234688997654375005790608560760415079605971661190214558366709321707<71> |