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emirp  and  evil n.

First numbers that belong to both sets:

17, 71, 113, 149, 311, 337, 347, 359, 389, 739, 751, 907, 937, 983, 1031, 1061, 1091, 1097, 1103, 1151, 1181, 1217, 1223, 1229, 1237, 1283, 1381, 1399, 1409, 1429, 1439, 1487, 1499, 1511, 1523, 1559, 1601, 1619, 1723, 1733, 1811, 1847, 1879, 1901, 1913, 1949, 3019, 3049, 3067, 3089, 3191, 3221, 3347, 3359, 3389, 3407, 3527, 3541, 3643, 3911, 3917, 3929, 7121, 7187, 7193, 7229, 7349, 7433, 7457, 7481, 7507, 7523, 7529, 7547, 7577, 7589, 7643, 7649, 7673, 7757, 7867, 7901, 7949, 9001, 9029, 9041, 9103, 9127, 9133, 9173, 9221, 9293, 9341, 9403, 9437, 9479, 9491, 9497, 9521, 9533, 9551, 9643, 9749, 9769, 9787, 9871, 9883, 9931, 9941, 9967, 10007, 10061, 10067, 10069, 10079, 10159, 10273, 10429, 10459, 10613, 10639, 10651, 10859, 10867, 10889, 10909, 10993, 11003, 11071, 11083, 11149, 11161, 11197, 11243, 11257, 11497, 11621, 11717, 11779, 11833, 11839, 11923, 11939, 11953, 11959, 11971, 12073, 12113, 12119, 12149, 12373, 12437, 12611, 12641, 12659, 12689, 12743, 12757, 12841, 12893, 12907, 13151, 13291, 13337, 13457, 13469, 13523, 13553, 13591, 13597, 13619, 13693, 13697, 13709, 13751, 13757, 13789, 13829, 13841, 13963, 14081, 14087, 14153, 14177, 14207, 14251, 14293, 14303, 14327, 14423, 14479, 14549, 14563, 14621, 14657, 14717, 14891, 14923, 14947, 15013, 15091, 15139, 15241, 15289, 15307, 15377, 15383, 15461, 15683, 15731, 15733, 15737, 15907, 15919, 16063, 16111, 16193, 16217, 16223, 16267, 16433, 16451, 16453, 16481, 16493, 16691, 16729, 16763, 16829, 16883, 16979, 17021, 17117, 17207, 17393, 17417, 17491, 17519, 17573, 17627, 17683, 17713, 17737, 17863, 17903, 17911, 17939, 18013, 18041, 18077, 18133, 18191, 18199, 18253, 18329, 18353, 18413, 18461, 18701, 18719, 18743, 18749, 18757, 18803, 18859, 18899, 18911, 19013, 19037, 19051, 19301, 19421, 19477, 19543, 19553, 19577, 19661, 19697, 19751, 19763.

Some larger examples :