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Chen prime  and  self n.

First numbers that belong to both sets:

3, 5, 7, 31, 53, 211, 233, 389, 479, 569, 659, 839, 1109, 1289, 1559, 2099, 2213, 2459, 2549, 2729, 3089, 3359, 3539, 3719, 3919, 4259, 4349, 4909, 4999, 5519, 6011, 6329, 6619, 6709, 6911, 7001, 7229, 7901, 8219, 8689, 8779, 9029, 9521, 9769, 9791, 10111, 10133, 10289, 10313, 10559, 10739, 11213, 11279, 11369, 11549, 12113, 12269, 12539, 13009, 13259, 13619, 14249, 14519, 15149, 15329, 15889, 16001, 16139, 16229, 16319, 16519, 16901, 17419, 17599, 17891, 17959, 18119, 18521, 18701, 18859, 19421, 19961, 20369, 20549, 20639, 21179, 21269, 22079, 22259, 22619, 23339, 23719, 24239, 24329, 24419, 24709, 24821, 24889, 25229, 25609, 26711, 26891, 27409, 27611, 27701, 27791, 28309, 28759, 28871, 28961, 29411, 29501, 29569, 29927, 30089, 30269, 30449, 30539, 31079, 31259, 32069, 32159, 33149, 33329, 33911, 34319, 34721, 35419, 35801, 36319, 36791, 37309, 37489, 37579, 37691, 37781, 38321, 38501, 38749, 38861, 39581, 39671, 39761, 39827, 40529, 41519, 41719, 42239, 42979, 43049, 43319, 43609, 43721, 43969, 44129, 44621, 44711, 45119, 45319, 45971, 46399, 46489, 46511, 46601, 46691, 47389, 47501, 47659, 47681, 47951, 48017, 48311, 48491, 48649, 49121, 49211, 49279, 49391, 49459, 49481, 49639, 49727, 50159, 51059, 51239, 51329, 51419, 52721, 52879, 52901, 53419, 53891, 53959, 54521, 54881, 55511, 55849, 55871, 56501, 56591, 56681, 57221, 57917, 58211, 58369, 58391, 58481, 58661, 58907, 58997, 59471, 59627, 60821, 60889, 61001, 61519, 61879, 61991, 62039, 62129, 62219, 62801, 62981, 63029, 63521, 63611, 63949, 64399, 64781, 64849, 64871, 65927, 65929, 65951, 66109, 66221, 66739, 66851, 67189, 67211, 67391, 67751, 67931, 68111, 68449, 68897, 69191, 69259, 69371, 69931, 70139, 70879, 71039, 71129, 71711, 72949, 73961, 74411, 74771, 74861, 74929, 75109, 75289, 75401, 76099, 76369, 76907, 77291, 77471, 78101, 78191, 78707, 78797, 78887, 78977, 79159, 79181, 79631, 79697, 79967.

Some larger examples :