n!!!!! + 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
* 657: | \[657!!!!!+1\] | 2531 × 224802451 × 1051174679 × 1461411720089732491<19> × [565335477776612492956528397975891043977234367026724973889668359706662630349778879650199713689167148799074276671375768331404038744711502354696302743591733111954113509379532090681172090780728833077565874401665364247736427867568545607827555940170485797628683008486549437381948893<276>] |