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pernicious n.  and  Sophie Germain prime

First numbers that belong to both sets:

3, 5, 11, 41, 131, 173, 179, 191, 233, 239, 251, 419, 431, 443, 491, 641, 653, 659, 719, 743, 761, 809, 911, 953, 1451, 1583, 1931, 2063, 2273, 2339, 2351, 2459, 2693, 2741, 2753, 2819, 2963, 2969, 3299, 3413, 3491, 3593, 3623, 3761, 3779, 3851, 4271, 4373, 4793, 5003, 5333, 5399, 5441, 6323, 6329, 6563, 6761, 7043, 7103, 7151, 7211, 7691, 7841, 8111, 8243, 8741, 8969, 9059, 9371, 9419, 10253, 10271, 10313, 10331, 10529, 10691, 10781, 11321, 11369, 11393, 11519, 11783, 11801, 11813, 11909, 12041, 12263, 12329, 12899, 13001, 13451, 13649, 14489, 14561, 14783, 14831, 15101, 15233, 15401, 15791, 15803, 16001, 16091, 16301, 16553, 16811, 16931, 17291, 17579, 17669, 17681, 18443, 18731, 18773, 19391, 20411, 20693, 20753, 20759, 20789, 21701, 21713, 21893, 22013, 22853, 23279, 24239, 24611, 24683, 24749, 24971, 25229, 25643, 26633, 26849, 26879, 26891, 27143, 27281, 27551, 27581, 27809, 28403, 28559, 28571, 28643, 28949, 30851, 31151, 31469, 31721, 32771, 32843, 32933, 33179, 33191, 33461, 33479, 33521, 33569, 33713, 34319, 34439, 34883, 34913, 34949, 35081, 35099, 35111, 35831, 35993, 36353, 36479, 36791, 36923, 37049, 37379, 37871, 38639, 38891, 39089, 39419, 39443, 39521, 39551, 39569, 39971, 40559, 40763, 41081, 41231, 41243, 41381, 41621, 41669, 41729, 42023, 42089, 42131, 42719, 42743, 43013, 43313, 43391, 43541, 43793, 44129, 44543, 44879, 44909, 45053, 45131, 45569, 45641, 46523, 46703, 46751, 47363, 47543, 47609, 47741, 48029, 48131, 48239, 48563, 48731, 48761, 49103, 49193, 49331, 49811, 49919, 50051, 50261, 50513, 51203, 52361, 53051, 53411, 53951, 54011, 54251, 54293, 54773, 54959, 55931, 56123, 56663, 56891, 57839, 57881, 58049, 58889, 59063, 59123, 59369, 59393, 59399, 59879, 60149, 60251, 60383, 60449, 60719, 60779, 61331, 61409, 61961, 62171, 62351, 62459, 63179, 63419, 63671, 63743, 63803, 63929, 64301, 64439, 64451.

Some larger examples :