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good prime  and  Ulam n.

First numbers that belong to both sets:

11, 53, 97, 431, 739, 3527, 4211, 4903, 6029, 7537, 8167, 9311, 10831, 15053, 16829, 17909, 20849, 22637, 23549, 27673, 29833, 30803, 32057, 35729, 38669, 43573, 43961, 47111, 47279, 48479, 56359, 56437, 65407, 69991, 73517, 79103, 80447, 84053, 94291, 98369, 101267, 108739, 114467, 115769, 120539, 128099, 128201, 128311, 132619, 134989, 136177, 143387, 148123, 148147, 148663, 150869, 156577, 156941, 159013, 159157, 168599, 169483, 175211, 175621, 175663, 175687, 176017, 181693, 181889, 191413, 201781, 204913, 205817, 205949, 207457, 216551, 217157, 218047, 236627, 238093, 254593, 261557, 264577, 267167, 268721, 295699, 300137, 300569, 300581, 302551, 311951, 313507, 317263, 318103, 327247, 340573, 340849, 345643, 346039, 360817, 361313, 361763, 382351, 388159, 426551, 430697, 430739, 448793, 453553, 485347, 487637, 503123, 503771, 504787, 505027, 535487, 540041, 540061, 545527, 556679, 562181, 569573, 580627, 584387, 599231, 606943, 629381, 631133, 639257, 639433, 642737, 644029, 644117, 669241, 669607, 669649, 677927, 678037, 690997, 699053, 707627, 718163, 719143, 719659, 728521, 750661, 757241, 758671, 759553, 790169, 790189, 793487, 816817, 818999, 821641, 840907, 846869, 874087, 878021, 878539, 885727, 885881, 890653, 904087, 904627, 916099, 947341, 967319, 967663, 967693, 980579, 980887, 984323, 987971, 990277, 999853, 1000117, 1004977, 1005187, 1018643, 1032341, 1033289, 1055713, 1055771, 1055801, 1062977, 1067441, 1072829, 1074251, 1074833, 1090151, 1092821, 1092887, 1104731, 1123181, 1123477, 1146697, 1146787, 1149487, 1155899, 1160111, 1160893, 1173743, 1175561, 1177997, 1179251, 1210747, 1235137, 1236953, 1245527, 1245683, 1278337, 1281773, 1305511, 1308497, 1315451, 1321349, 1335157, 1338331, 1372913, 1374257, 1375723, 1377749, 1384661, 1384813, 1392197, 1393883, 1417301, 1424257, 1444411, 1444477, 1461283, 1471499, 1476149, 1476791, 1486003, 1486057, 1486687, 1532543, 1533083, 1552289, 1552333, 1552501, 1555013, 1588747, 1591841, 1602059, 1602269, 1665523, 1666261, 1685381, 1690043, 1697737, 1724263, 1726189, 1738127, 1762427, 1771981, 1777423, 1790209, 1803023, 1803059, 1804381, 1804447, 1817969, 1818013, 1820261, 1839283, 1841057, 1853177, 1903859, 1904467, 1906087, 1906109, 1972031, 1972097, 1975019, 1995517, 1995649, 2002151.

Some larger examples :