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de Polignac n.  and  self n.

First numbers that belong to both sets:

1, 905, 1087, 1199, 1649, 1783, 1829, 1985, 2213, 2279, 2503, 2683, 3539, 4327, 4573, 4663, 4843, 5405, 5923, 6193, 6283, 6463, 6821, 7319, 7431, 7811, 7901, 8621, 8981, 9521, 10199, 10357, 10379, 10447, 10513, 10873, 10963, 11279, 11347, 11437, 11549, 11593, 11729, 12427, 12517, 13147, 13169, 13393, 13619, 14047, 14227, 14249, 14383, 14473, 14585, 14765, 14809, 14921, 15037, 15059, 15127, 15149, 15217, 15373, 15419, 15957, 16027, 16117, 16543, 17039, 17083, 17735, 18611, 18881, 18971, 19961, 20437, 20617, 20639, 21247, 21359, 21583, 21673, 21763, 22147, 22327, 22439, 22663, 23339, 24217, 24463, 24665, 24733, 24821, 24889, 25027, 25139, 25229, 25273, 25295, 25453, 25723, 25925, 27029, 27163, 27253, 27343, 27611, 27791, 28333, 28399, 28781, 28893, 29323, 29345, 29771, 30313, 30403, 30427, 30449, 30539, 30629, 31237, 31259, 31417, 31619, 31843, 32047, 32069, 32203, 33011, 33149, 33373, 34183, 34273, 34721, 35263, 35443, 35645, 36073, 36433, 36971, 37243, 37535, 37669, 37691, 38053, 38143, 38501, 38861, 39065, 39491, 40147, 40213, 40259, 40933, 41227, 41293, 42373, 42485, 43093, 43565, 43633, 43879, 43901, 44083, 44129, 44263, 45073, 45433, 45791, 46041, 46243, 46421, 46601, 47345, 47681, 48043, 48581, 48671, 48715, 49391, 49571, 50159, 50203, 50317, 50339, 50429, 51011, 51127, 51193, 51283, 51329, 51395, 51419, 51531, 51823, 52049, 52139, 52273, 52319, 52475, 52721, 53195, 53711, 53801, 54073, 54275, 54813, 55153, 55421, 55423, 55511, 56411, 56681, 57017, 57087, 57581, 57829, 57941, 58123, 58907, 58931, 59291, 59493, 59651, 59741, 59831, 60059, 60215, 60329, 60419, 61139, 61229, 61453, 62105, 62129, 62219, 62801, 62981, 64243, 64423, 64647, 64961, 65053, 65927, 66133, 66221, 66491, 66739, 67033, 67211, 67301, 67369, 67391, 67661, 67751, 68111, 68381, 69101, 69281, 69371, 69551, 69641, 69731, 70117, 70229, 70723, 70811, 70991, 71533, 71621, 71623, 71801, 72073, 72455, 72521, 72523, 72701, 73243.

Some larger examples :