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emirp  and  happy n.

First numbers that belong to both sets:

13, 31, 79, 97, 167, 709, 739, 761, 907, 937, 1009, 1033, 1151, 1487, 1511, 1733, 1847, 1933, 3019, 3067, 3083, 3109, 3301, 3319, 3371, 3391, 3463, 3643, 3803, 7457, 7481, 7547, 7589, 7603, 7841, 9001, 9013, 9103, 9133, 9857, 10009, 10039, 10067, 10151, 10177, 10247, 10333, 10457, 10487, 11149, 11159, 11197, 11243, 11423, 11719, 11971, 12149, 12437, 12491, 12743, 12841, 13009, 13457, 13499, 13697, 13757, 13841, 13903, 13933, 14057, 14081, 14087, 14207, 14327, 14387, 14449, 14549, 14551, 14821, 14831, 14939, 15101, 15299, 15377, 15461, 15541, 15679, 15737, 16007, 16063, 16127, 16217, 16451, 16603, 16937, 17033, 17207, 17443, 17573, 17627, 17669, 17713, 17827, 17911, 18041, 18253, 18413, 18743, 18757, 18899, 19333, 19421, 19763, 30029, 30139, 30319, 30323, 30367, 30643, 30661, 30931, 31033, 31307, 31393, 31481, 31771, 32009, 32257, 32303, 32369, 32411, 32693, 32887, 32983, 33013, 33029, 33071, 33301, 33391, 33589, 33931, 34147, 34211, 34471, 34603, 34721, 34781, 34897, 34919, 35227, 35281, 35569, 35983, 36037, 36061, 36209, 36607, 36791, 36809, 37489, 37571, 37619, 38239, 38287, 38329, 38923, 38953, 39313, 39419, 39623, 39749, 39799, 39829, 70009, 70061, 70241, 70271, 70313, 70457, 70589, 70663, 70937, 71069, 71261, 71537, 71569, 72161, 72253, 72341, 72379, 72577, 72671, 72871, 73063, 73421, 73517, 73751, 73849, 73907, 73961, 74143, 74201, 75041, 75169, 75223, 75401, 75407, 75431, 75731, 75767, 75781, 76001, 76303, 76757, 77101, 77351, 77527, 77587, 78041, 78059, 78283, 78341, 78401, 78439, 78577, 78823, 79111, 79229, 79349, 79399, 79631, 79843, 79939, 90001, 90007, 90023, 90031, 90089, 90263, 90863, 91303, 91493, 91673, 91711, 91943, 92003, 92033, 92297, 92383, 92893, 93001, 93103, 93283, 93487, 93941, 93997, 94111, 94121, 94397, 94441, 94541, 94793, 94837, 95087, 95111, 96017, 96157, 96323, 96517, 96553, 96671, 97327, 97651, 98009, 98473, 98507, 98533, 99251, 99397, 99431.

Some larger examples :