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cyclic n.  and  unprimeable n.

First numbers that belong to both sets:

515, 535, 895, 1135, 1145, 1335, 1345, 1415, 1465, 1645, 1685, 1765, 1795, 1855, 1895, 2045, 2185, 2195, 2405, 2495, 2515, 3055, 3095, 3145, 3235, 3265, 3665, 3745, 3785, 3815, 3995, 4035, 4085, 4145, 4195, 4315, 4385, 4415, 4435, 4535, 4685, 4745, 4765, 5045, 5065, 5215, 5245, 5315, 5365, 5465, 5495, 5545, 5605, 5615, 5765, 5965, 6185, 6235, 6415, 6515, 6535, 6645, 6755, 6815, 6935, 7085, 7115, 7135, 7145, 7165, 7265, 7445, 7465, 7615, 7735, 7765, 7805, 7835, 7895, 7985, 8045, 8135, 8155, 8185, 8255, 8335, 8345, 8395, 8455, 8485, 8495, 8615, 8795, 8905, 8915, 8985, 9035, 9085, 9115, 9215, 9265, 9365, 9385, 9445, 9565, 9705, 9865, 9895, 9985, 9995, 10015, 10085, 10235, 10415, 10445, 10645, 10745, 10765, 10915, 11015, 11035, 11185, 11305, 11335, 11345, 11455, 11665, 11845, 11915, 11995, 12065, 12085, 12135, 12185, 12295, 12335, 12355, 12365, 12385, 12665, 12935, 12995, 13015, 13055, 13085, 13205, 13235, 13285, 13345, 13405, 13435, 13505, 13745, 13865, 13895, 13945, 13985, 14065, 14095, 14165, 14185, 14215, 14315, 14395, 14495, 14585, 14605, 14615, 14705, 14915, 14995, 15045, 15115, 15155, 15485, 15505, 15535, 15595, 15635, 15695, 15755, 15835, 15845, 15865, 16015, 16045, 16285, 16295, 16405, 16465, 16535, 16595, 16715, 16735, 16795, 16865, 16915, 17005, 17065, 17245, 17285, 17635, 17645, 17695, 17755, 17815, 17845, 17945, 17965, 18005, 18035, 18295, 18335, 18385, 18565, 18845, 18885, 18905, 18965, 18985, 19045, 19115, 19295, 19345, 19495, 19615, 19645, 19785, 19835, 19955, 20035, 20095, 20135, 20155, 20195, 20465, 20495, 20585, 20605, 20765, 20795, 20915, 20995, 21095, 21295, 21365, 21445, 21455, 21535, 21635, 21695, 21745, 21905, 21985, 22045, 22235, 22315, 22355, 22415, 22555, 22585, 22595, 22685, 22795, 22835, 22845, 22885, 22915, 22985, 23215, 23245, 23285, 23305, 23385, 23515, 23615, 23645, 23695, 23795, 23935.

Some larger examples :