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Chen prime  and  emirp

First numbers that belong to both sets:

13, 17, 31, 37, 71, 107, 113, 149, 157, 167, 179, 199, 311, 337, 347, 359, 389, 701, 743, 751, 761, 769, 937, 941, 953, 971, 983, 991, 1009, 1031, 1061, 1091, 1097, 1109, 1151, 1193, 1201, 1217, 1229, 1259, 1283, 1301, 1381, 1399, 1409, 1439, 1471, 1487, 1499, 1511, 1559, 1583, 1601, 1619, 1669, 1733, 1847, 1901, 1913, 1949, 1979, 3011, 3083, 3089, 3191, 3203, 3221, 3251, 3257, 3271, 3299, 3347, 3359, 3371, 3389, 3407, 3467, 3511, 3527, 3541, 3719, 3767, 3803, 3821, 3851, 3889, 3917, 3929, 7043, 7121, 7177, 7193, 7229, 7253, 7321, 7349, 7433, 7457, 7481, 7507, 7529, 7547, 7561, 7589, 7649, 7757, 7817, 7901, 7949, 9001, 9011, 9029, 9041, 9209, 9221, 9227, 9257, 9341, 9437, 9467, 9479, 9491, 9521, 9533, 9551, 9661, 9769, 9791, 9857, 9941, 9967, 10007, 10039, 10061, 10067, 10079, 10091, 10247, 10343, 10391, 10457, 10487, 10499, 10639, 10711, 10739, 10781, 10859, 10867, 10889, 10891, 10909, 11057, 11071, 11159, 11197, 11447, 11489, 11497, 11551, 11579, 11587, 11621, 11657, 11699, 11717, 11719, 11731, 11777, 11783, 11789, 11839, 11897, 11903, 11909, 11927, 11939, 11969, 11981, 12071, 12107, 12113, 12149, 12227, 12269, 12437, 12611, 12641, 12659, 12713, 12743, 12757, 12809, 12893, 13009, 13043, 13151, 13163, 13259, 13267, 13337, 13441, 13457, 13469, 13477, 13499, 13553, 13619, 13709, 13751, 13757, 13789, 13829, 13841, 14057, 14071, 14081, 14087, 14107, 14177, 14207, 14251, 14303, 14387, 14447, 14449, 14519, 14549, 14591, 14621, 14629, 14633, 14657, 14717, 14843, 14879, 14891, 14897, 14939, 14957, 15053, 15101, 15131, 15149, 15227, 15241, 15497, 15511, 15527, 15679, 15683, 15731, 15737, 15791, 15907, 16001, 16007, 16103, 16127, 16249, 16427, 16451, 16481, 16493, 16691, 16829, 16937, 16943, 16979, 17021, 17033, 17047, 17207, 17209, 17417, 17519, 17579, 17599, 17669, 17681.

Some larger examples :