n!! - 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
* 312: | \[312!!-1\] | 311 × 2141 × 275534023 × 20023460363<11> × 4754830030245389<16> × [3906927021287369072145424078453573670576776514209514999815172807570170407182131285408083284637741658663687496223348971127600251489232359156701049471329863992396991621953225709095287394918269767116995321439558447856891245410501072317300429940875993878273075109040268843141773220181509<283>] |