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Sophie Germain prime  and  strong prime

First numbers that belong to both sets:

11, 29, 41, 179, 191, 239, 251, 281, 419, 431, 641, 659, 719, 809, 1019, 1031, 1049, 1229, 1289, 1451, 1481, 1733, 1901, 1931, 1973, 2063, 2129, 2141, 2339, 2459, 2549, 2741, 2819, 2969, 3299, 3329, 3359, 3389, 3449, 3491, 3539, 3761, 3821, 3851, 4019, 4073, 4211, 4271, 4349, 4391, 4481, 4871, 5039, 5051, 5231, 5279, 5441, 5501, 5639, 5711, 5741, 5849, 6113, 6131, 6269, 6449, 6521, 6551, 6563, 6761, 6899, 7103, 7121, 7151, 7211, 7349, 7901, 8111, 8513, 8663, 8969, 9029, 9059, 9221, 9371, 9419, 9629, 9689, 10061, 10091, 10271, 10313, 10331, 10529, 10589, 10709, 10781, 10883, 11171, 11369, 11393, 11519, 11549, 11579, 11699, 11801, 11831, 11939, 12041, 12263, 12791, 12821, 13001, 13451, 13553, 13901, 14009, 14081, 14249, 14321, 14561, 14621, 14699, 14879, 14939, 15101, 15269, 16001, 16301, 16811, 16823, 17159, 17183, 17291, 17351, 17579, 17681, 18041, 18131, 18191, 18773, 18899, 19301, 19373, 19553, 19661, 19709, 19751, 19889, 19913, 19991, 20063, 20249, 20441, 20771, 20921, 20939, 21011, 21089, 21179, 21221, 21341, 21611, 21701, 22271, 22343, 22433, 22469, 22481, 22541, 22853, 23321, 23561, 23669, 23909, 24239, 24509, 24611, 24749, 25073, 25229, 25523, 25601, 25799, 25841, 25913, 26111, 26879, 26891, 27281, 27479, 27539, 27581, 27893, 27983, 28019, 28403, 28571, 28643, 28751, 28859, 28901, 28949, 29021, 29201, 30269, 30389, 30671, 30689, 30773, 30851, 31151, 31319, 31469, 31721, 31793, 32003, 32141, 32159, 32531, 32561, 32771, 32933, 33023, 33179, 33191, 33479, 33521, 33713, 33749, 33809, 34253, 34913, 35081, 35099, 35831, 35993, 36383, 36629, 36761, 36791, 36929, 37013, 37049, 37181, 37871, 37991, 38039, 38231, 38459, 38669, 38723, 38861, 38891, 39089, 39239, 39659, 39971, 40343, 41231, 41381, 41609, 41729, 42071, 42131, 42221, 42719, 42821, 42923, 43013, 43313, 43391, 43541, 43649, 43661, 43691, 43943, 44111, 44129, 44249.

Some larger examples :