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evil n.  and  Sophie Germain prime

First numbers that belong to both sets:

3, 5, 23, 29, 53, 83, 89, 113, 281, 293, 359, 509, 593, 683, 1013, 1031, 1049, 1103, 1223, 1229, 1289, 1409, 1439, 1481, 1499, 1511, 1559, 1601, 1733, 1811, 1889, 1901, 1973, 2003, 2039, 2069, 2129, 2141, 2393, 2399, 2549, 2699, 2903, 3329, 3359, 3389, 3449, 3539, 3863, 3911, 4211, 4349, 4391, 4409, 4481, 4733, 4871, 4919, 4943, 5081, 5171, 5231, 5279, 5303, 5639, 5711, 5741, 5849, 5903, 6053, 6113, 6131, 6173, 6263, 6269, 6449, 6491, 6521, 6551, 6581, 6983, 7121, 7193, 7349, 7433, 7643, 7649, 7901, 8069, 8093, 8273, 8513, 8663, 8693, 9029, 9221, 9293, 9473, 9479, 9539, 9629, 9689, 10061, 10589, 10613, 10709, 10799, 10883, 11171, 11549, 11939, 12011, 12101, 12119, 12203, 12653, 12671, 12791, 12821, 13313, 13463, 13553, 13619, 13763, 13901, 13913, 14081, 14153, 14159, 14303, 14321, 14621, 14669, 14741, 15173, 15569, 15629, 15773, 16253, 16421, 16493, 16673, 16823, 16883, 17159, 17183, 17333, 17351, 17939, 17981, 18041, 18131, 18149, 18191, 18233, 18341, 18461, 18803, 18899, 19301, 19319, 19553, 19559, 19661, 19709, 19751, 19889, 19913, 19919, 19991, 20063, 20249, 20369, 20441, 20771, 20879, 20921, 20939, 20963, 21011, 21089, 21149, 21221, 21383, 21611, 21803, 22079, 22259, 22271, 22409, 22433, 22541, 22751, 22943, 23321, 23561, 23603, 23753, 23819, 23981, 24281, 24473, 24509, 24551, 25073, 25601, 25673, 25703, 25799, 25841, 25913, 25919, 26111, 26189, 26459, 26501, 26573, 26993, 27479, 27743, 27773, 27893, 27983, 28001, 28019, 28499, 28751, 28793, 28901, 28961, 29033, 29201, 29453, 29531, 29723, 29873, 30269, 30323, 30389, 30449, 30671, 30689, 30773, 30983, 31253, 31319, 31793, 31799, 31859, 32003, 32009, 32141, 32159, 32381, 32531, 32561, 32573, 32633, 32789, 33053, 33119, 33623, 33749, 33809, 33941, 34253, 34631, 35933, 36191, 36629, 36821, 36929, 37013, 37139, 37181, 37253, 37853, 37991, 38039, 38183.

Some larger examples :