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odious n.  and  twin primes

First numbers that belong to both sets:

7, 11, 13, 19, 31, 41, 59, 61, 73, 103, 107, 109, 137, 151, 179, 181, 191, 193, 199, 227, 229, 239, 241, 271, 283, 313, 419, 421, 431, 433, 463, 521, 569, 601, 617, 641, 659, 661, 809, 823, 827, 829, 859, 883, 1019, 1021, 1033, 1051, 1063, 1153, 1231, 1279, 1291, 1301, 1321, 1451, 1453, 1483, 1609, 1667, 1669, 1697, 1721, 1787, 1789, 1877, 1931, 1933, 1951, 1999, 2027, 2029, 2081, 2087, 2111, 2113, 2131, 2143, 2237, 2267, 2269, 2311, 2339, 2341, 2383, 2551, 2591, 2657, 2687, 2711, 2731, 2789, 2801, 2969, 2999, 3119, 3121, 3169, 3251, 3253, 3257, 3299, 3301, 3331, 3361, 3371, 3373, 3391, 3463, 3467, 3469, 3529, 3559, 3583, 3673, 3767, 3821, 3851, 3853, 3919, 3931, 4001, 4019, 4021, 4051, 4091, 4093, 4129, 4159, 4219, 4231, 4243, 4259, 4261, 4271, 4273, 4339, 4421, 4483, 4519, 4639, 4649, 4723, 4787, 4789, 4799, 4801, 4969, 5011, 5023, 5099, 5101, 5281, 5419, 5441, 5477, 5501, 5641, 5659, 5743, 5851, 5867, 5869, 5881, 6091, 6199, 6271, 6299, 6301, 6361, 6451, 6553, 6569, 6659, 6661, 6689, 6701, 6761, 6779, 6781, 6791, 6871, 6947, 6949, 6959, 6961, 7129, 7211, 7213, 7307, 7309, 7331, 7333, 7351, 7459, 7561, 7591, 7759, 7879, 7951, 8011, 8089, 8219, 8221, 8231, 8291, 8293, 8387, 8389, 8429, 8539, 8599, 8627, 8629, 8819, 8821, 8837, 8861, 8969, 8999, 9011, 9013, 9043, 9241, 9283, 9343, 9419, 9421, 9433, 9439, 9463, 9631, 9679, 9721, 9767, 9857, 9929, 10009, 10039, 10091, 10093, 10139, 10141, 10271, 10301, 10331, 10333, 10457, 10499, 10501, 10529, 10711, 10891, 10939, 11057, 11069, 11117, 11159, 11353, 11489, 11551, 11699, 11701, 11719, 11777, 11831, 11969, 12041, 12071, 12107, 12109, 12161, 12239, 12241, 12251, 12253, 12379, 12539, 12541, 12823.

Some larger examples :