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good prime  and  Sophie Germain prime

First numbers that belong to both sets:

5, 11, 29, 41, 53, 179, 191, 251, 419, 431, 593, 641, 809, 1031, 1973, 2063, 2339, 3299, 3449, 3821, 4211, 4481, 4871, 5639, 6263, 6521, 6551, 6563, 6761, 8513, 8663, 9371, 10061, 10091, 10589, 11699, 14321, 14699, 15269, 16811, 16823, 17291, 18899, 19373, 19889, 19913, 22541, 25523, 25913, 28403, 28571, 30671, 35831, 38669, 39089, 41603, 43943, 47279, 48479, 48731, 49103, 50741, 52511, 53591, 54251, 54401, 55661, 58889, 61331, 61469, 62459, 65099, 67121, 69809, 73523, 74699, 75149, 75161, 77261, 77471, 79769, 79811, 80651, 80669, 84299, 86111, 88463, 91079, 91121, 98369, 98711, 103391, 106103, 108863, 114599, 114641, 115751, 120539, 127481, 128099, 128321, 148139, 148331, 148853, 148859, 156671, 156941, 159671, 160619, 162251, 165311, 168449, 175211, 175391, 176201, 184823, 184829, 185051, 190523, 191441, 196643, 201401, 201473, 205031, 205391, 206879, 207479, 216719, 219353, 227453, 234161, 236609, 237683, 237689, 241313, 243461, 253229, 253343, 262049, 262109, 262121, 266663, 273881, 274061, 274661, 274811, 278543, 288989, 293999, 300623, 302573, 312023, 315449, 316133, 317321, 318179, 324053, 327401, 334289, 335999, 336029, 336491, 350699, 360749, 374639, 374669, 382229, 383483, 387911, 388109, 388691, 391613, 391679, 404951, 405221, 417479, 417491, 426551, 429083, 429119, 429449, 430649, 448853, 449129, 467063, 467399, 467471, 485819, 486023, 504929, 515639, 524801, 540041, 541193, 548189, 548393, 568979, 569573, 569711, 575573, 575579, 580631, 591599, 592199, 599213, 599303, 600233, 603719, 610391, 610409, 610541, 611801, 611939, 628679, 629243, 639491, 643403, 643421, 644051, 644123, 646823, 657911, 659843, 668471, 672779, 678329, 699053, 700079, 701219, 701399, 701951, 702269, 704003, 707669, 719633, 723029, 728681, 744599, 745931, 747401, 748463, 750653, 758099, 759431, 760079, 762893, 763403, 775601, 783119, 789941, 790169, 792023, 803849, 808343, 837923, 837929, 838391, 842063, 846341, 854849, 855581, 860309, 861491, 873989, 874619, 875261, 904019, 904661, 906179, 914351, 916031, 916049, 923309, 937571, 949583, 956843, 960983, 967259, 967289, 980393.

Some larger examples :