n!!!!! + 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
* 351: | \[351!!!!!+1\] | 115209225629<12> × [2247280146602132213485380286215271791983503002581171118561518344641331790596478455818962462991261899170450744020868865625944895553927801013<139>] |