n!!!! - 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
355: | \[355!!!!-1\] | 2 × 10833847 × 12627301717816651<17> × 6135089706421795647324274875981250256006499289489629084186439556531300766751194219584730667752340630404108216936054268050980408684188917372638191675352083332062807821<166> |