n!!!!! - 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
* 348: | \[348!!!!!-1\] | 331 × 2699 × 32383223 × 3774866325550583<16> × [113846238469279018394955758624897009062831979146435013455100859010700346462975363165498135874809024448591472973025582663<120>] |