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Sophie Germain prime  and  twin primes

First numbers that belong to both sets:

3, 5, 11, 29, 41, 179, 191, 239, 281, 419, 431, 641, 659, 809, 1019, 1031, 1049, 1229, 1289, 1451, 1481, 1931, 2129, 2141, 2339, 2549, 2969, 3299, 3329, 3359, 3389, 3539, 3821, 3851, 4019, 4271, 4481, 5231, 5279, 5441, 5501, 5639, 5741, 5849, 6131, 6269, 6449, 6551, 6761, 7211, 7349, 8969, 9419, 9629, 10091, 10271, 10331, 10529, 10709, 11171, 11549, 11699, 11831, 11939, 12041, 12821, 13001, 13901, 14009, 14081, 14249, 14321, 14561, 15269, 17291, 17579, 17681, 18041, 18131, 19751, 19889, 19991, 20441, 20771, 21011, 21611, 22271, 22481, 22541, 23561, 23669, 23909, 25601, 25799, 26111, 26879, 26891, 27281, 27479, 27539, 27581, 28571, 28751, 29021, 30269, 30389, 30851, 31151, 31319, 31721, 32141, 32531, 32561, 33179, 33749, 33809, 35081, 36791, 36929, 37991, 38459, 38669, 39239, 41231, 41609, 42071, 42221, 43541, 43649, 44129, 44699, 45119, 45179, 46181, 46349, 46589, 47741, 48479, 48731, 49331, 49919, 50021, 50051, 50261, 50591, 50969, 52289, 52361, 53549, 53591, 54011, 54401, 55439, 55631, 55661, 55931, 56099, 56531, 56891, 56909, 56921, 57329, 58451, 58601, 59021, 60761, 61331, 61469, 62981, 63419, 63839, 64301, 64451, 65099, 65171, 66749, 68111, 68279, 68489, 68819, 69029, 70181, 70379, 70979, 72101, 72269, 74099, 74201, 74381, 74729, 74759, 75389, 76001, 76259, 76421, 76871, 77261, 77711, 78509, 78779, 79151, 79559, 79811, 79841, 80669, 80681, 81281, 81701, 81929, 82139, 82529, 82721, 82889, 83339, 83399, 84629, 85829, 85931, 86111, 86291, 87149, 87221, 87539, 87959, 88661, 88811, 91079, 91139, 92681, 92861, 93239, 93479, 93911, 94151, 95789, 97001, 98321, 98561, 98639, 98711, 100361, 100799, 101999, 102299, 102911, 103091, 103391, 104231, 104759, 105359, 106121, 106451, 108011, 109139, 109841, 111029, 111731, 112289, 112571, 112919, 113759, 114599, 114641, 115151, 115469, 115781, 115859, 117041, 117191, 117329, 117371, 117839, 117989, 118169, 119771, 119849, 119921, 119981, 120941, 121631.

Some larger examples :