n!! + 1
Table
Format: small prime × proven prime<size> × (probable prime)<size> × [composite]<size> × {unknown}<size>
* 253: | \[253!!+1\] | 29 × 21157 × 59357 × 3836471 × 1085947283 × 18423409853087<14> × 20415430829738239<17> × [25444276516062188261351855375409798737197068416237807037469190746957028924601085078689658769828751824321554449811970438294877813638189186885115652185101468227509338635539134189206669862835012023<194>] |