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Chen prime  and  de Polignac n.

First numbers that belong to both sets:

127, 149, 251, 337, 509, 599, 701, 809, 877, 977, 1019, 1259, 1619, 1759, 1777, 2213, 2579, 2789, 2843, 2879, 2909, 2999, 3119, 3181, 3187, 3299, 3539, 3637, 3779, 4001, 4229, 4271, 4567, 4649, 4889, 5077, 5099, 5303, 5737, 6247, 6269, 6449, 6521, 6637, 6659, 6791, 6869, 7109, 7151, 7177, 7331, 7417, 7517, 7547, 7901, 8087, 8387, 8429, 8527, 8849, 8861, 8887, 9239, 9431, 9521, 9929, 9941, 10007, 10061, 10079, 10391, 10607, 10781, 10949, 11069, 11171, 11279, 11411, 11549, 11579, 11789, 11909, 12007, 12203, 12239, 12251, 12401, 12479, 12791, 13001, 13217, 13451, 13469, 13619, 13679, 13799, 13841, 13859, 13901, 14009, 14081, 14107, 14249, 14303, 14347, 14437, 14489, 14879, 15101, 15149, 15161, 15359, 15401, 15551, 15641, 15809, 16361, 16787, 17021, 17047, 17077, 17489, 17519, 17579, 17669, 17909, 17921, 17957, 18089, 18427, 18517, 18719, 18787, 18869, 18899, 18911, 18959, 19139, 19163, 19319, 19379, 19583, 19709, 19819, 19889, 19949, 19961, 20201, 20287, 20639, 20693, 20717, 21101, 21599, 21683, 21701, 21839, 22481, 22567, 22691, 22769, 22817, 22859, 22901, 23017, 23099, 23321, 23339, 23417, 23531, 23669, 24179, 24281, 24371, 24509, 24683, 24697, 24821, 24889, 24977, 25057, 25229, 25349, 25561, 25799, 25841, 26489, 26759, 27127, 27197, 27437, 27449, 27479, 27611, 27791, 27941, 28109, 28181, 28289, 28349, 28499, 28571, 28597, 28837, 29297, 29669, 29759, 30109, 30307, 30341, 30449, 30539, 30671, 30689, 30727, 30757, 30839, 30851, 30911, 31259, 31357, 31469, 31511, 31817, 32069, 32257, 32309, 32647, 32993, 33071, 33149, 33161, 33179, 33191, 33791, 33797, 33809, 34019, 34259, 34421, 34457, 34631, 34679, 34721, 34919, 35051, 35437, 35447, 35729, 35897, 35951, 36479, 36677, 36767, 37691, 38189, 38371, 38459, 38501, 38557, 38651, 38861, 38917, 39239, 39251, 39509, 39521, 39659, 39779, 39821, 39839, 39869, 39929, 39971, 40037, 40189, 40289, 40387, 40897, 41549.

Some larger examples :