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emirp  and  weak prime

First numbers that belong to both sets:

13, 31, 73, 113, 167, 199, 337, 359, 389, 709, 743, 761, 941, 953, 971, 983, 1021, 1033, 1069, 1097, 1109, 1153, 1193, 1201, 1217, 1231, 1237, 1259, 1279, 1283, 1321, 1381, 1409, 1429, 1439, 1453, 1499, 1559, 1583, 1601, 1669, 1723, 1789, 1811, 1831, 1879, 1913, 1933, 1979, 3023, 3049, 3067, 3083, 3089, 3121, 3169, 3191, 3221, 3271, 3301, 3347, 3373, 3391, 3463, 3469, 3541, 3583, 3643, 3803, 3853, 3889, 3911, 7027, 7043, 7193, 7219, 7253, 7433, 7459, 7481, 7507, 7529, 7561, 7577, 7643, 7649, 7673, 7879, 7951, 7963, 9001, 9013, 9161, 9209, 9227, 9241, 9257, 9293, 9349, 9403, 9421, 9439, 9467, 9479, 9497, 9521, 9551, 9661, 9679, 9721, 9749, 9769, 9791, 9833, 9931, 10009, 10039, 10069, 10079, 10247, 10273, 10321, 10333, 10343, 10429, 10459, 10487, 10613, 10639, 10711, 10739, 10867, 10891, 10909, 10939, 10993, 11003, 11071, 11161, 11243, 11329, 11353, 11423, 11447, 11551, 11621, 11701, 11719, 11779, 11783, 11789, 11833, 11839, 11909, 11927, 11959, 11971, 12073, 12109, 12113, 12119, 12149, 12241, 12253, 12269, 12289, 12301, 12437, 12491, 12553, 12619, 12641, 12659, 12743, 12763, 12799, 12809, 12829, 12893, 12919, 12983, 13009, 13151, 13163, 13267, 13297, 13469, 13477, 13499, 13523, 13597, 13619, 13693, 13697, 13711, 13759, 13789, 13841, 13903, 13933, 14057, 14087, 14107, 14153, 14177, 14207, 14221, 14251, 14303, 14323, 14327, 14423, 14449, 14551, 14563, 14593, 14629, 14633, 14657, 14717, 14831, 14891, 14897, 14929, 14957, 15091, 15139, 15149, 15241, 15263, 15289, 15377, 15383, 15497, 15511, 15643, 15649, 15683, 15733, 15791, 15937, 15973, 16007, 16063, 16073, 16103, 16111, 16193, 16433, 16453, 16481, 16493, 16573, 16651, 16747, 16763, 16883, 16943, 17033, 17209, 17393, 17491, 17519, 17573, 17599, 17627, 17669, 17683, 17713, 17737, 17749, 17839, 17863, 17911, 17923, 17939, 17959, 18013, 18133, 18199.

Some larger examples :