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nude n.  and  unprimeable n.

First numbers that belong to both sets:

324, 515, 624, 848, 1144, 1266, 1332, 1335, 1344, 1412, 1416, 1464, 1644, 1715, 1764, 1926, 1962, 2184, 2196, 2322, 2328, 2364, 2488, 2824, 3144, 3264, 3288, 3666, 3816, 3996, 4144, 4164, 4184, 4412, 4416, 4824, 4848, 4896, 6432, 6624, 6648, 6816, 7112, 7266, 7448, 8136, 8184, 8488, 8496, 8616, 9144, 9216, 9864, 11122, 11124, 11128, 11184, 11222, 11224, 11226, 11535, 11664, 11848, 11872, 11916, 12122, 12124, 12126, 12128, 12132, 12184, 12312, 12336, 12366, 12384, 12444, 12448, 12624, 12666, 12816, 12864, 12996, 13116, 13236, 13272, 13344, 13776, 13896, 14112, 14124, 14128, 14136, 14184, 14212, 14232, 14316, 14616, 15115, 15155, 15575, 15715, 16164, 16326, 16464, 16626, 16716, 17248, 17262, 18248, 18336, 18384, 18624, 18648, 18816, 18824, 18848, 18872, 18888, 18936, 19116, 19224, 19296, 19368, 21112, 21336, 21366, 21424, 21444, 21448, 21624, 21636, 22164, 22212, 22236, 22266, 22326, 22332, 22412, 22416, 22424, 22824, 22848, 22888, 22896, 23124, 23232, 23244, 23424, 23616, 24144, 24212, 24216, 24264, 24276, 24384, 24648, 24724, 24816, 24864, 26124, 26136, 26364, 26616, 26964, 27132, 27384, 27412, 27972, 28144, 28248, 28368, 28488, 28824, 28888, 29736, 31116, 31164, 31344, 31362, 31368, 31416, 31632, 31824, 31932, 32124, 32136, 32166, 32226, 32244, 32316, 32436, 32664, 32676, 32922, 33126, 33132, 33135, 33264, 33366, 33384, 33432, 33444, 33555, 33666, 33696, 33984, 34116, 34164, 34224, 34248, 34344, 34416, 34776, 34824, 34992, 36126, 36144, 36288, 36324, 36336, 36366, 36396, 36444, 36612, 36666, 36816, 36864, 37296, 37926, 38136, 38424, 38472, 38688, 39816, 39915, 39996, 41124, 41128, 41272, 41316, 41328, 41364, 41424, 41436, 41488, 41824, 41832, 42112, 42124, 42128, 42144, 42212, 42216, 42244, 42248, 42264, 42312, 42384, 42412, 42424, 42624, 42636, 42816, 42888, 42912, 43128, 43164, 43212, 43248, 43344, 43368, 43464, 43764, 43824, 43848, 44144, 44212, 44232, 44316, 44328.

Some larger examples :