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de Polignac n.  and  good prime

First numbers that belong to both sets:

127, 149, 251, 331, 599, 809, 1087, 1597, 1867, 1973, 2203, 2683, 2999, 3163, 3299, 3433, 4001, 4229, 6521, 6547, 6637, 6659, 7517, 8087, 9371, 9391, 9613, 10007, 10061, 11239, 12239, 12373, 13679, 14407, 14533, 15013, 15217, 17827, 17909, 18899, 18911, 19139, 19379, 19889, 19961, 20707, 20717, 21487, 22691, 23531, 25561, 27611, 27673, 28571, 28597, 29833, 29983, 30671, 30757, 31957, 35729, 35951, 36433, 38557, 38651, 40423, 40693, 41947, 43933, 44497, 45943, 46133, 46993, 47041, 47279, 47293, 47497, 48407, 48731, 48757, 48973, 50741, 50767, 51193, 51329, 51341, 51419, 52501, 52529, 54251, 54311, 55603, 55661, 55763, 58889, 60607, 61211, 61253, 61331, 63299, 65099, 65353, 65407, 65519, 66449, 66491, 67033, 69997, 70117, 70823, 70841, 71143, 71233, 74017, 74699, 75133, 75161, 77137, 77261, 77417, 77471, 79087, 79549, 79769, 80147, 80669, 84127, 84299, 84313, 84389, 86011, 88463, 88643, 88799, 89519, 91121, 91127, 92173, 92551, 94397, 98179, 98407, 98887, 98893, 100333, 101107, 103289, 103511, 104471, 106087, 106207, 106261, 110527, 110557, 111487, 114571, 115547, 119503, 119653, 120551, 120661, 120823, 127241, 127597, 128201, 128311, 128339, 131701, 132229, 132589, 136207, 143443, 144139, 144247, 145391, 148361, 150767, 150881, 156577, 156671, 159389, 159403, 159457, 160541, 160579, 162251, 162493, 165287, 166237, 166541, 166597, 168851, 169483, 175211, 175601, 175631, 175687, 176201, 176299, 176317, 177787, 178469, 181603, 184993, 185051, 185429, 185467, 189149, 189337, 190573, 191441, 191447, 194681, 195043, 196499, 197257, 200771, 204913, 205949, 206177, 206909, 207187, 207923, 216551, 216647, 216731, 217199, 218047, 227081, 227453, 228299, 228419, 234161, 234187, 236377, 236681, 237851, 238151, 241229, 243073, 243461, 244109, 244121, 244297, 246469, 253361, 253417, 254593, 254699, 257219, 262109, 262121, 263009, 263167, 264731, 266587, 266633, 266821, 267187, 267401, 274829, 275881, 280487, 289019, 293983, 295663, 295751, 295837, 298993, 299011, 300581, 302759, 302969, 303283, 311957, 312007, 312029, 313507, 315247, 315373.

Some larger examples :