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Chen prime  and  happy n.

First numbers that belong to both sets:

7, 13, 19, 23, 31, 109, 139, 167, 239, 263, 293, 379, 409, 487, 563, 617, 653, 683, 761, 863, 881, 937, 1009, 1039, 1151, 1277, 1427, 1481, 1487, 1511, 1607, 1697, 1733, 1847, 2003, 2039, 2111, 2309, 2333, 2339, 2393, 2417, 2557, 2741, 2963, 3083, 3137, 3329, 3371, 3637, 3709, 3779, 3797, 3803, 3907, 4127, 4157, 4217, 4271, 4441, 4447, 4481, 4517, 4721, 4817, 4871, 5147, 5417, 5471, 5477, 5741, 5879, 5897, 5987, 6197, 6329, 6337, 6637, 6661, 6701, 6791, 6803, 6899, 6971, 7039, 7127, 7309, 7331, 7451, 7457, 7481, 7541, 7547, 7589, 7793, 7937, 8081, 8147, 8369, 8597, 8741, 8969, 9001, 9377, 9587, 9689, 9857, 10039, 10067, 10211, 10247, 10427, 10457, 10487, 10607, 10847, 11159, 11197, 11467, 11483, 11519, 11681, 11719, 12011, 12149, 12347, 12437, 12743, 12959, 13009, 13339, 13421, 13457, 13499, 13577, 13679, 13757, 13841, 13967, 14057, 14081, 14087, 14207, 14321, 14347, 14387, 14437, 14449, 14549, 14561, 14783, 14813, 14939, 15101, 15641, 15679, 15737, 15887, 16007, 16097, 16127, 16451, 16741, 16937, 17027, 17033, 17207, 17569, 17609, 17669, 18041, 18047, 18587, 18839, 18899, 19421, 19889, 19997, 20063, 20147, 20177, 20369, 20393, 20639, 20693, 20717, 20771, 20899, 21011, 21101, 21143, 21149, 21341, 21347, 21407, 21419, 21491, 21599, 21617, 21767, 22549, 22621, 22861, 23039, 23369, 23417, 23447, 23609, 23663, 23741, 23887, 23977, 24107, 24137, 24317, 24371, 24683, 24859, 25057, 25561, 26171, 26177, 26267, 26309, 26393, 26627, 26669, 26711, 26821, 26903, 27017, 27107, 27299, 27397, 27431, 27611, 27617, 27701, 27967, 28387, 28463, 28837, 29033, 29063, 29297, 29303, 29411, 29633, 29927, 30029, 30109, 30137, 30269, 30689, 30713, 30869, 30977, 31247, 31307, 31481, 31547, 31699, 31769, 31847, 32069, 32141, 32257, 32309, 32369, 32411, 32609, 33071, 33107, 33359, 33391, 33589, 33931, 34127, 34147, 34157.

Some larger examples :