n!!!! + 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
* 408: | \[408!!!!+1\] | 103 × 271 × 401 × 270111715369<12> × [8176171765337192990804965914394536950152519061262434932598756004308535008083944729640874346622342429026294784936158296632020230259773995278185991904791433684427757294610841118807386688790861499275752524033<205>] |