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emirp  and  strong prime

First numbers that belong to both sets:

17, 37, 71, 79, 97, 107, 149, 179, 311, 347, 701, 739, 751, 769, 907, 937, 967, 991, 1009, 1031, 1061, 1091, 1151, 1181, 1213, 1229, 1249, 1301, 1399, 1471, 1487, 1523, 1597, 1619, 1657, 1733, 1741, 1847, 1867, 1901, 1949, 3011, 3019, 3109, 3163, 3203, 3251, 3257, 3299, 3319, 3343, 3359, 3371, 3389, 3407, 3433, 3467, 3511, 3527, 3571, 3613, 3697, 3719, 3767, 3821, 3851, 3917, 3929, 7057, 7121, 7177, 7187, 7207, 7229, 7297, 7321, 7349, 7457, 7547, 7589, 7603, 7681, 7687, 7699, 7717, 7757, 7817, 7867, 7901, 7927, 7949, 9011, 9029, 9041, 9103, 9127, 9133, 9173, 9221, 9341, 9437, 9491, 9533, 9547, 9601, 9613, 9643, 9781, 9787, 9803, 9857, 9883, 9923, 9941, 9967, 10007, 10061, 10067, 10091, 10151, 10159, 10177, 10391, 10453, 10457, 10499, 10651, 10781, 10859, 10889, 10987, 11057, 11083, 11149, 11159, 11197, 11257, 11489, 11579, 11587, 11593, 11657, 11677, 11699, 11717, 11777, 11897, 11923, 11939, 11953, 11969, 11981, 12071, 12107, 12227, 12323, 12373, 12577, 12611, 12689, 12697, 12713, 12757, 12907, 13147, 13159, 13259, 13291, 13337, 13441, 13513, 13553, 13591, 13709, 13751, 13757, 13781, 13829, 13873, 13963, 14029, 14071, 14081, 14143, 14293, 14387, 14431, 14447, 14479, 14519, 14549, 14557, 14591, 14621, 14713, 14821, 14843, 14879, 14923, 14939, 14947, 15013, 15053, 15101, 15131, 15227, 15299, 15307, 15349, 15461, 15493, 15527, 15541, 15601, 15661, 15667, 15679, 15731, 15737, 15919, 16001, 16127, 16217, 16249, 16267, 16451, 16547, 16603, 16691, 16699, 16729, 16829, 16879, 16979, 17011, 17021, 17041, 17117, 17203, 17207, 17383, 17417, 17443, 17467, 17579, 17681, 17747, 17827, 17903, 17909, 18041, 18077, 18089, 18169, 18191, 18307, 18329, 18427, 18439, 18539, 18671, 18691, 18743, 18773, 18787, 18859, 18899, 18911, 19001, 19181, 19231, 19249, 19301, 19421, 19531, 19541, 19553, 19661, 19681, 19697.

Some larger examples :