n!!!!! + 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
310: | \[310!!!!!+1\] | 727 × 356479 × 268118749 × 7888592157879869775299819909<28> × 1244920427265779797859135256600150462340169051345891715986330771371149604889109708617<85> |