n!!!!! - 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
288: | \[288!!!!!-1\] | 1128694340029<13> × 31481383661169483883<20> × 1806772948737848434306141022906328559483<40> × 167756023164988009183109609368601727241912491443<48> |