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good prime  and  odious n.

First numbers that belong to both sets:

11, 37, 41, 59, 67, 97, 127, 179, 191, 223, 227, 251, 307, 331, 419, 431, 541, 557, 563, 569, 587, 641, 727, 733, 809, 929, 967, 1009, 1087, 1213, 1367, 1423, 1543, 1597, 1867, 1987, 1993, 2063, 2237, 2267, 2339, 2521, 2531, 2609, 2647, 2657, 2677, 2687, 2999, 3163, 3251, 3299, 3433, 3457, 3511, 3821, 3847, 3907, 4001, 4201, 4507, 4621, 4861, 4903, 5381, 5647, 6043, 6067, 6547, 6563, 6637, 6659, 6689, 6761, 6779, 6947, 7411, 7517, 8161, 8167, 8209, 8219, 8521, 8677, 8689, 8999, 9277, 9319, 9337, 9371, 9397, 9613, 10091, 10597, 10847, 10853, 11057, 11657, 11677, 11699, 11777, 11807, 11897, 12197, 12227, 12239, 12473, 12487, 12889, 14243, 14369, 14387, 14401, 14407, 14519, 14533, 14699, 14713, 15053, 15217, 15227, 15269, 16411, 16417, 16547, 16811, 16879, 17291, 17317, 17377, 17383, 17783, 17827, 17909, 19001, 19139, 19207, 19373, 19379, 19417, 20707, 20849, 20981, 21139, 21481, 21487, 21557, 22531, 22613, 22691, 22697, 23497, 23531, 24841, 24907, 24917, 25087, 25111, 25117, 25523, 25537, 25561, 25577, 26669, 26681, 27397, 27407, 27611, 27673, 27689, 28403, 28537, 28571, 28597, 29833, 30631, 30637, 30757, 31139, 32297, 32969, 33287, 33311, 33329, 34123, 35729, 35797, 35801, 35831, 35951, 35963, 36433, 36467, 36523, 36671, 38113, 38543, 38557, 38593, 38651, 39089, 40423, 40427, 40471, 40693, 40697, 40739, 40751, 40759, 40801, 40813, 40819, 41039, 41131, 41141, 41177, 41843, 41849, 41879, 41941, 43889, 44483, 44497, 45943, 46021, 46049, 46091, 46141, 46399, 46993, 47041, 47051, 47087, 47111, 48311, 48337, 48397, 48463, 48731, 48757, 48973, 49103, 50767, 50821, 50833, 51109, 51131, 51193, 51329, 51341, 51407, 51419, 53591, 54251, 54319, 55579, 55603, 55787, 56359, 56377, 56431, 56467, 56473, 58889, 58897, 61211, 61283, 61331, 61441, 62459, 62467, 63241, 63277, 64553, 64567, 65027, 65089, 65099, 65353, 65407.

Some larger examples :