n!!!!! - 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
352: | \[352!!!!!-1\] | 8923 × 24735617 × 12292409013827069<17> × 1264602472057268578010879<25> × 94392294133292487026330999891305103<35> × 3878737011439108709268118427483225288322538196058946887925929089<64> |