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de Polignac n.  and  inconsummate n.

First numbers that belong to both sets:

1271, 1541, 1649, 2993, 3149, 3665, 3697, 4151, 4271, 4649, 4811, 4841, 5303, 6119, 6637, 6659, 7331, 7431, 8159, 9371, 9581, 9641, 9959, 10237, 10327, 10357, 10379, 10409, 10607, 10697, 11541, 11549, 11993, 12371, 12671, 12881, 13217, 13961, 14021, 14051, 14381, 14681, 14765, 14879, 14975, 15037, 15041, 15149, 15187, 15299, 15419, 15641, 16177, 16181, 16409, 17021, 17147, 17327, 17437, 17651, 17759, 17921, 19163, 19259, 19631, 19649, 19709, 19807, 20321, 20437, 20591, 20651, 20717, 20957, 21037, 21701, 22481, 23651, 24281, 24731, 24963, 25331, 25481, 25841, 25925, 25979, 26009, 26489, 26807, 27029, 27507, 27611, 28037, 28109, 28137, 28181, 28259, 28331, 28499, 28781, 28799, 28865, 29101, 29159, 29219, 29369, 29381, 29609, 29741, 30281, 30307, 30409, 30415, 30449, 30587, 30851, 30911, 31025, 31031, 31061, 31091, 31237, 31259, 31469, 31511, 31687, 31747, 31817, 32047, 32069, 32407, 32467, 32621, 32677, 32767, 32879, 33071, 33179, 33209, 33699, 34181, 34259, 34421, 34537, 34787, 35051, 35399, 35437, 35447, 35459, 35699, 35897, 35909, 35951, 35957, 36035, 36187, 36209, 36247, 36401, 36457, 36479, 36503, 36581, 36677, 36759, 36767, 36869, 36971, 37003, 37033, 37087, 37349, 37409, 37535, 37559, 37841, 37859, 37931, 38137, 38159, 38189, 38489, 39251, 39269, 39393, 39607, 39641, 40037, 40049, 40259, 40307, 40331, 40577, 40781, 40841, 40859, 40903, 40923, 40927, 40979, 41045, 41171, 41309, 41423, 41639, 41819, 41939, 42113, 42599, 42623, 42737, 42989, 43207, 43379, 43709, 43987, 44255, 44531, 44543, 44609, 44849, 44927, 45423, 45851, 45893, 45935, 46001, 46181, 46259, 46537, 46661, 46709, 46985, 47037, 47327, 47489, 47519, 47681, 47699, 47735, 48101, 48131, 48239, 48371, 48407, 48437, 48671, 48965, 49837, 50207, 50489, 51479, 51941, 52807, 53009, 53147, 54059, 54251, 54287, 54809, 55031, 55193, 56339, 56651, 56977, 57107, 57481, 57581, 57607, 57659, 57677, 58181, 58361, 58865, 58991, 59021, 59159, 59207, 59493.

Some larger examples :