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good prime  and  lucky n.

First numbers that belong to both sets:

37, 67, 127, 223, 307, 331, 541, 727, 739, 937, 1009, 1087, 1543, 1597, 1987, 2647, 3163, 3433, 3847, 4201, 4441, 4621, 8161, 9151, 9277, 9613, 10597, 11047, 11239, 11677, 11887, 12373, 12487, 14293, 14407, 14713, 15073, 15217, 15259, 16417, 19207, 19417, 21139, 24763, 24907, 25117, 25147, 25561, 27427, 31147, 36451, 38149, 38167, 40459, 40471, 41947, 43933, 46021, 46141, 46399, 47287, 48751, 50767, 54319, 55603, 56359, 56377, 56437, 58897, 60589, 62467, 65353, 73291, 74143, 77137, 79531, 84121, 88789, 92143, 92347, 93871, 94291, 98179, 98317, 98893, 100333, 103387, 104677, 106273, 108751, 110419, 110431, 110527, 111409, 111427, 114547, 114571, 119653, 127591, 127597, 131431, 132229, 132511, 132523, 132607, 135271, 136189, 136303, 136333, 143401, 148663, 151141, 156589, 156619, 159457, 160579, 162493, 162523, 166597, 175687, 176317, 184993, 185677, 189139, 189307, 195691, 197203, 197233, 204913, 206779, 207169, 209173, 216751, 217111, 218077, 227977, 228049, 234181, 236377, 237967, 238141, 241303, 244087, 263077, 264553, 266599, 274777, 280183, 293983, 299011, 299281, 299881, 300187, 300481, 311677, 315349, 315517, 316189, 317257, 318103, 324097, 327193, 339517, 339583, 339601, 339613, 340027, 343237, 345643, 361159, 370411, 382507, 388891, 389743, 407137, 407203, 414199, 416947, 429211, 429463, 448519, 448597, 449077, 449107, 463213, 467119, 467611, 485311, 485893, 486307, 488203, 494341, 503197, 503593, 512521, 515227, 540061, 545371, 545437, 545527, 545863, 547357, 558421, 558457, 567601, 568963, 569599, 601747, 601801, 606913, 606943, 607921, 611827, 628651, 631357, 631843, 633739, 633751, 639253, 642853, 653461, 658051, 659497, 663517, 668527, 671887, 671911, 678199, 678367, 678577, 683251, 691681, 691687, 699931, 699943, 703837, 703849, 703861, 719671, 730447, 747277, 748453, 758071, 758179, 758227, 762721, 763339, 763381, 764887, 764947, 776749, 786823, 786859, 809719, 816763, 816811, 840703, 840907, 841849, 846661, 846721, 846913, 863767, 864007, 874063, 874087, 878011, 885679, 885721, 885769, 904441, 904483, 904627, 906259, 914161, 916831, 917083, 917611, 923023, 923107.

Some larger examples :