n!!! - 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
168: | \[168!!!-1\] | 1579 × 751613 × 19823245747<11> × 1445343771130801<16> × 828542549059102783<18> × 13207537520278369855190138656151507995917072289237<50> |