n!!!!! + 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
223: | \[223!!!!!+1\] | 5333 × 134353 × 11029297 × 3778695379 × 322799539745008177308487<24> × 51526123802370093057154331016272661401<38> |