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odious n.  and  Sophie Germain prime

First numbers that belong to both sets:

2, 11, 41, 131, 173, 179, 191, 233, 239, 251, 419, 431, 443, 491, 641, 653, 659, 719, 743, 761, 809, 911, 953, 1019, 1451, 1583, 1931, 2063, 2273, 2339, 2351, 2459, 2543, 2693, 2741, 2753, 2819, 2939, 2963, 2969, 3023, 3299, 3413, 3491, 3593, 3623, 3761, 3779, 3803, 3821, 3851, 4019, 4073, 4271, 4373, 4793, 5003, 5039, 5051, 5333, 5399, 5441, 5501, 6101, 6323, 6329, 6563, 6761, 6899, 7043, 7079, 7103, 7151, 7211, 7541, 7691, 7823, 7841, 7883, 8111, 8243, 8741, 8951, 8969, 9059, 9371, 9419, 9791, 10091, 10163, 10253, 10271, 10313, 10331, 10529, 10691, 10733, 10781, 11321, 11369, 11393, 11471, 11519, 11579, 11699, 11783, 11801, 11813, 11831, 11909, 12041, 12263, 12329, 12899, 12923, 12959, 13001, 13049, 13229, 13451, 13649, 13883, 14009, 14249, 14489, 14561, 14699, 14783, 14831, 14879, 14939, 15101, 15161, 15233, 15269, 15401, 15791, 15803, 15923, 16001, 16091, 16301, 16553, 16811, 16931, 17291, 17579, 17669, 17681, 18443, 18731, 18773, 19163, 19373, 19391, 19433, 20393, 20411, 20693, 20753, 20759, 20789, 21179, 21341, 21419, 21701, 21713, 21893, 22013, 22133, 22343, 22349, 22469, 22481, 22853, 23099, 23279, 23339, 23459, 23669, 23909, 24203, 24239, 24611, 24683, 24749, 24971, 25229, 25523, 25643, 26633, 26849, 26879, 26891, 27143, 27281, 27539, 27551, 27581, 27809, 28403, 28559, 28571, 28643, 28859, 28949, 29021, 29339, 29363, 29483, 30851, 31019, 31151, 31469, 31649, 31721, 32771, 32843, 32933, 33023, 33179, 33191, 33461, 33479, 33521, 33569, 33713, 33773, 34283, 34319, 34439, 34883, 34913, 34949, 35069, 35081, 35099, 35111, 35291, 35573, 35831, 35993, 35999, 36083, 36251, 36353, 36383, 36479, 36563, 36761, 36791, 36923, 37049, 37379, 37619, 37871, 38231, 38459, 38639, 38891, 39089, 39419, 39443, 39521, 39551, 39569, 39779, 39971, 39983, 40559, 40763, 41081, 41231, 41243, 41381, 41399, 41621, 41669, 41729, 41969.

Some larger examples :