n!!!!! - 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
317: | \[317!!!!!-1\] | 5 × 463 × 3727 × 47869 × 273281 × 67519729 × 219500279 × 60648791447<11> × 141559344450263<15> × 4778555059792157327405670046921380379<37> × 37194990776026542710113748513995234891<38> |