n!!!!! + 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
* 404: | \[404!!!!!+1\] | 5 × 73142289552539<14> × [2336040957193887712684555895584413647856435982998918482200970641705409105875510506245742737440552966408201521132309484656776606341795073929897837535756475706349239<163>] |