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Chen prime  and  Sophie Germain prime

First numbers that belong to both sets:

2, 3, 5, 11, 23, 29, 41, 53, 83, 89, 113, 131, 179, 191, 233, 239, 251, 281, 293, 359, 419, 431, 443, 491, 509, 641, 653, 659, 683, 719, 743, 761, 809, 911, 953, 1019, 1031, 1049, 1229, 1289, 1409, 1439, 1451, 1481, 1499, 1511, 1559, 1583, 1601, 1733, 1889, 1901, 1931, 2003, 2039, 2069, 2129, 2141, 2339, 2351, 2393, 2459, 2543, 2549, 2699, 2741, 2939, 2963, 2969, 3299, 3329, 3359, 3389, 3413, 3491, 3539, 3593, 3761, 3779, 3803, 3821, 3851, 3863, 4019, 4211, 4271, 4349, 4391, 4409, 4481, 4733, 4871, 5039, 5051, 5171, 5231, 5279, 5303, 5399, 5441, 5501, 5639, 5711, 5741, 5849, 5903, 6101, 6113, 6131, 6269, 6329, 6449, 6491, 6521, 6551, 6581, 6761, 6899, 7043, 7079, 7121, 7151, 7193, 7211, 7349, 7433, 7541, 7649, 7901, 8069, 8093, 8663, 8741, 8951, 8969, 9029, 9221, 9419, 9479, 9629, 9689, 9791, 10061, 10091, 10271, 10313, 10331, 10529, 10709, 10781, 10799, 11171, 11369, 11519, 11549, 11579, 11699, 11783, 11831, 11909, 11939, 12011, 12041, 12203, 12653, 12791, 12821, 12959, 13001, 13049, 13229, 13313, 13451, 13463, 13553, 13619, 13763, 13883, 13901, 14009, 14081, 14249, 14303, 14321, 14489, 14561, 14621, 14669, 14699, 14741, 14783, 14879, 14939, 15101, 15161, 15269, 15401, 15569, 15791, 16001, 16253, 16421, 16493, 17159, 17291, 17333, 17579, 17669, 17681, 18041, 18131, 18149, 18461, 18803, 18899, 19163, 19301, 19319, 19553, 19559, 19709, 19751, 19889, 19919, 19991, 20063, 20369, 20393, 20411, 20441, 20693, 20759, 20771, 20789, 20939, 21011, 21149, 21179, 21221, 21341, 21419, 21611, 21701, 22079, 22259, 22271, 22409, 22469, 22481, 22541, 22751, 23099, 23279, 23321, 23339, 23459, 23561, 23603, 23669, 23753, 23909, 23981, 24239, 24281, 24509, 24551, 24611, 24683, 24749, 25229, 25601, 25799, 25841, 26111, 26189, 26459, 26501, 26849, 26879, 26891.

Some larger examples :