n!!!!! + 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
362: | \[362!!!!!+1\] | 341191 × 3038049979142675803013537<25> × 156615900186895390422076694130400644706868589319314545536071257826070204436371290378325405719178888921780125724816931262101399<126> |