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Duffinian n.  and  unprimeable n.

First numbers that belong to both sets:

324, 325, 512, 515, 535, 625, 845, 1075, 1135, 1265, 1352, 1355, 1415, 1465, 1505, 1645, 1675, 1682, 1685, 1765, 1855, 1922, 1925, 2048, 2075, 2105, 2405, 2485, 2515, 2585, 2825, 3055, 3145, 3155, 3175, 3235, 3265, 3425, 3485, 3505, 3565, 3665, 3685, 3745, 3755, 3785, 3955, 3995, 4105, 4165, 4315, 4385, 4415, 4418, 4435, 4535, 4555, 4575, 4615, 4685, 4715, 4745, 4765, 4775, 4825, 4855, 4925, 5065, 5125, 5255, 5315, 5375, 5455, 5465, 5495, 5615, 5618, 5675, 5755, 5765, 5915, 5965, 6185, 6400, 6415, 6505, 6515, 6535, 6625, 6724, 6728, 6755, 6925, 7115, 7135, 7165, 7265, 7275, 7385, 7405, 7442, 7465, 7615, 7655, 7765, 7775, 7835, 7985, 8135, 8155, 8185, 8255, 8305, 8335, 8395, 8405, 8450, 8485, 8615, 8635, 8855, 8875, 8905, 8915, 9075, 9115, 9216, 9305, 9355, 9365, 9385, 9485, 9505, 9565, 9575, 9655, 9755, 9775, 9865, 9955, 9985, 10015, 10025, 10055, 10082, 10085, 10205, 10375, 10385, 10404, 10405, 10415, 10675, 10765, 10805, 10816, 10825, 11015, 11035, 11105, 11185, 11335, 11405, 11605, 11645, 11664, 11665, 11725, 11755, 11795, 11845, 11855, 11915, 12025, 12055, 12085, 12125, 12175, 12185, 12335, 12355, 12365, 12385, 12625, 12775, 12815, 12835, 12865, 12875, 12995, 13025, 13055, 13075, 13085, 13115, 13135, 13235, 13285, 13345, 13355, 13375, 13405, 13435, 13655, 13735, 13778, 13895, 13955, 13975, 13985, 14045, 14125, 14135, 14165, 14185, 14215, 14275, 14335, 14375, 14450, 14495, 14575, 14585, 14605, 14675, 14705, 14905, 15005, 15025, 15115, 15205, 15488, 15505, 15655, 15695, 15835, 15842, 15895, 15965, 16015, 16025, 16165, 16175, 16205, 16285, 16325, 16355, 16375, 16405, 16505, 16535, 16585, 16685, 16715, 16735, 16775, 16805, 16855, 16865, 16955, 17065, 17215, 17225, 17275, 17285, 17305, 17365, 17424, 17425, 17455, 17525, 17615, 17635, 17672, 17675, 17755, 17845, 17945, 17965, 18005.

Some larger examples :