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de Polignac n.  and  sphenic n.

First numbers that belong to both sets:

2465, 4503, 4543, 5405, 5467, 6853, 7535, 8789, 9581, 10199, 10235, 10619, 11039, 11137, 11285, 11627, 11921, 12595, 12727, 12733, 12749, 12805, 13091, 13409, 13735, 14231, 14467, 14605, 15113, 15521, 16027, 16031, 16165, 16405, 16629, 16849, 17437, 17759, 18487, 18565, 18685, 19057, 19135, 19345, 20195, 20383, 20909, 21359, 21637, 21793, 22919, 23443, 24963, 25753, 25783, 25993, 26065, 26429, 26609, 26789, 27379, 27507, 28135, 28137, 28259, 28483, 28865, 29197, 29309, 29323, 29495, 29971, 30401, 30793, 30955, 31229, 31297, 31537, 31565, 31871, 31901, 32705, 32767, 33299, 33341, 33397, 33449, 33699, 33839, 34181, 34561, 35189, 35305, 35399, 35485, 35715, 36613, 36869, 36883, 37135, 37297, 37453, 39065, 39277, 39479, 39491, 40105, 40745, 40859, 40985, 41107, 41293, 41561, 41591, 41665, 41819, 42067, 42343, 42485, 42763, 42883, 43529, 43537, 43571, 43901, 44099, 44255, 44363, 44429, 44759, 44849, 44885, 45059, 45073, 45101, 45103, 45479, 45733, 45899, 46041, 47173, 47345, 47519, 48085, 48269, 48581, 48671, 48965, 49029, 49469, 49585, 49693, 49777, 49837, 49933, 49979, 50297, 50407, 50479, 50713, 51027, 51119, 51127, 51395, 51531, 51557, 51569, 51779, 51815, 52049, 52415, 52649, 52805, 53009, 53227, 53365, 53447, 53755, 53801, 54223, 54353, 54899, 55319, 55979, 55993, 56021, 56289, 56353, 56833, 57017, 57071, 57343, 58123, 58349, 58535, 58597, 58865, 58919, 59189, 59493, 59549, 59815, 59831, 59917, 59969, 60005, 60059, 60071, 60329, 60367, 60973, 61237, 61369, 61415, 61439, 61541, 61693, 61919, 61945, 62345, 62615, 63403, 63583, 63779, 63899, 63935, 64207, 64277, 64477, 64543, 64657, 64753, 64841, 64897, 64961, 65263, 65593, 65773, 65823, 65879, 65941, 66283, 66847, 66929, 66997, 67015, 67039, 67301, 67379, 67873, 68381, 68419, 68593, 68735, 68847, 69085, 69161, 69293, 69641, 69671, 69839, 69989, 70235, 70477, 70705, 71533, 71617, 71621, 71755, 72013, 72265, 72455, 72457, 72523, 72699, 72787, 73439, 73511, 73513, 73627.

Some larger examples :