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Chen prime  and  Honaker prime

First numbers that belong to both sets:

131, 263, 1039, 1049, 1091, 1301, 1361, 1913, 2141, 2441, 2591, 2719, 2729, 3137, 3559, 4091, 4357, 4397, 4703, 5009, 5507, 5701, 5711, 5741, 5801, 6311, 6737, 6827, 6971, 7481, 8011, 10247, 10559, 10711, 11071, 11731, 12277, 12347, 13007, 13127, 13217, 13339, 13367, 13457, 14437, 14447, 14843, 15671, 15761, 16451, 16661, 17159, 17189, 18041, 21617, 22277, 22613, 22807, 23059, 23531, 25229, 25339, 26119, 26189, 26209, 26309, 27059, 29243, 31391, 31517, 32059, 34259, 34471, 35027, 35149, 35227, 35537, 36217, 37019, 37039, 37117, 37493, 38011, 38711, 40361, 40427, 40637, 41131, 41141, 41491, 41801, 42509, 42727, 42737, 43781, 44221, 44417, 45119, 45181, 45191, 45821, 46147, 46237, 47147, 48119, 49031, 50417, 51131, 51263, 52051, 53309, 53591, 54617, 55049, 55541, 56807, 57059, 57089, 57119, 58321, 58411, 60251, 60601, 61253, 62057, 62617, 63031, 64151, 64817, 65831, 68147, 68813, 68903, 69257, 69383, 69911, 70139, 70379, 70489, 71261, 72019, 72337, 73009, 73607, 74231, 75503, 77237, 77249, 77291, 77711, 78007, 78017, 78437, 80657, 81199, 81239, 82217, 83231, 85133, 88661, 91019, 91571, 92627, 92791, 92861, 93097, 94151, 95111, 96053, 96443, 97103, 97151, 97231, 97241, 98911, 99041, 100279, 100559, 101939, 103979, 105331, 106031, 108037, 109103, 109331, 110129, 111347, 111491, 112163, 112927, 113327, 113357, 113417, 113591, 113891, 115571, 115601, 115631, 116159, 116189, 120709, 122471, 123701, 125117, 126143, 129221, 131009, 132607, 133241, 133451, 133811, 134741, 136139, 136207, 136217, 136237, 136337, 136621, 139133, 139409, 139703, 143291, 143483, 145441, 145661, 145721, 149183, 150287, 151337, 151537, 152851, 154211, 155017, 155027, 156361, 157307, 160507, 160583, 161149, 162109, 162119, 163127, 163481, 164621, 170447, 170711, 170851, 171641, 171671, 171761, 171811, 171881, 173137, 173207, 174091, 174767, 175229, 175853, 180281, 181211, 181913, 182417, 183091, 183119, 183451, 183461, 184187, 184901, 185149, 185327, 185711, 186239, 186707, 187127, 187417, 187721, 191039, 191341, 191507, 191627.

Some larger examples :