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happy n.  and  strong prime

First numbers that belong to both sets:

79, 97, 239, 331, 367, 379, 397, 487, 617, 673, 739, 881, 907, 937, 1009, 1151, 1277, 1427, 1447, 1481, 1487, 1607, 1663, 1697, 1733, 1847, 2063, 2111, 2309, 2333, 2339, 2741, 2833, 2851, 3019, 3079, 3109, 3319, 3329, 3371, 3607, 3907, 4127, 4157, 4217, 4271, 4441, 4447, 4481, 4517, 4721, 4751, 4871, 5147, 5227, 5417, 5471, 5477, 5527, 5569, 5741, 5821, 5879, 5897, 6037, 6163, 6197, 6337, 6353, 6389, 6637, 6673, 6701, 6733, 6791, 6899, 7039, 7127, 7331, 7451, 7457, 7547, 7589, 7603, 8081, 8147, 8521, 8597, 8929, 8963, 8969, 9007, 9103, 9133, 9587, 9689, 9829, 9857, 10067, 10151, 10177, 10211, 10427, 10457, 10663, 10771, 10847, 10903, 11113, 11149, 11159, 11197, 11251, 11311, 11467, 11483, 11519, 12143, 12473, 12511, 12941, 13033, 13093, 13241, 13309, 13411, 13679, 13757, 14081, 14281, 14321, 14387, 14407, 14549, 14561, 14813, 14821, 14939, 15101, 15121, 15299, 15461, 15541, 15641, 15679, 15737, 15787, 15877, 15887, 16127, 16217, 16417, 16451, 16603, 16741, 16759, 16811, 17027, 17207, 17317, 17443, 17569, 17827, 18041, 18047, 18143, 18743, 18839, 18899, 19259, 19421, 19889, 20063, 20147, 20639, 20717, 20771, 21011, 21101, 21341, 21481, 21491, 21599, 21767, 21787, 22129, 22229, 22381, 22783, 23039, 23369, 23417, 23447, 23581, 23663, 23741, 23827, 23887, 23977, 24071, 24107, 24317, 24371, 25057, 25111, 25183, 25237, 25453, 25561, 25657, 26171, 26227, 26309, 26339, 26557, 26627, 26669, 26711, 27107, 27253, 27397, 27611, 27697, 27817, 27823, 27883, 28051, 28081, 28387, 28463, 28513, 28643, 28723, 28789, 28837, 29221, 29297, 29383, 29833, 29983, 30109, 30133, 30137, 30269, 30293, 30319, 30553, 30661, 30689, 30803, 30869, 30931, 31033, 31177, 31247, 31307, 31663, 31769, 31847, 32141, 32257, 32369, 32411, 32609, 32779, 32797, 32839, 32983, 33013, 33023, 33071, 33083, 33107, 33301, 33391, 33931, 34127, 34157, 34211, 34313.

Some larger examples :