n!!!!! - 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
308: | \[308!!!!!-1\] | 107377 × 2138407883989275993539<22> × 2870649912881242301087<22> × 133139538048127140009643786048108740891500815677771326532918600895792174611106043<81> |