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lucky n.  and  twin primes

First numbers that belong to both sets:

3, 7, 13, 31, 43, 73, 151, 193, 241, 283, 349, 421, 433, 463, 601, 619, 643, 823, 883, 1021, 1093, 1231, 1291, 1303, 1723, 1879, 1933, 2083, 2113, 2239, 2311, 2593, 2689, 2971, 3121, 3259, 3301, 3559, 3931, 4003, 4129, 4483, 4519, 4801, 4969, 5233, 5419, 5503, 5641, 5851, 5869, 6271, 6301, 6553, 6661, 6763, 6871, 7129, 7333, 7459, 7489, 7549, 7591, 7951, 8089, 8221, 8233, 8539, 9421, 9631, 10009, 10069, 10459, 10501, 10531, 10891, 11059, 11173, 11491, 11833, 12163, 12379, 13009, 13219, 13681, 13693, 13723, 13759, 13831, 14449, 15271, 16981, 17209, 17389, 17581, 17749, 18043, 18049, 18253, 18523, 19081, 19543, 19963, 19993, 20149, 20359, 20509, 20551, 20773, 20899, 21013, 21193, 21613, 21739, 21841, 22039, 22093, 22369, 23041, 23293, 23563, 23671, 23689, 24181, 25033, 25171, 25309, 26251, 26263, 26683, 26881, 26893, 27061, 27283, 27409, 27541, 27691, 27751, 27793, 28351, 30013, 30559, 30871, 31081, 31249, 31723, 31849, 32119, 32533, 32563, 32803, 32833, 33151, 33181, 33289, 33349, 33601, 33769, 34129, 34213, 34261, 34513, 35449, 36469, 36529, 37339, 37549, 37813, 38461, 38611, 38653, 38713, 38749, 38923, 39043, 39841, 40153, 40849, 42073, 42643, 43543, 43579, 43789, 43891, 44383, 45121, 45139, 45181, 45343, 46309, 47419, 47743, 48481, 48541, 48679, 49123, 49279, 49921, 50023, 50053, 50551, 50893, 51349, 51421, 51871, 52291, 52861, 52903, 53593, 53719, 54403, 54583, 55219, 55621, 55633, 55819, 55903, 56209, 56269, 56479, 56533, 58171, 58393, 59443, 59473, 60259, 60763, 60889, 61153, 62143, 62191, 62299, 62929, 62983, 64189, 64579, 64921, 65029, 65101, 65173, 65521, 65839, 66109, 67189, 67579, 67759, 68113, 68209, 68449, 69259, 70459, 70573, 71329, 71341, 72223, 72649, 73363, 74101, 74161, 74509, 74761, 75211, 75391, 75709, 75991, 76423, 76831, 76873, 77263, 77269, 77689, 78193, 78511, 79153, 79561, 80209, 80473, 80671, 80683, 80749.

Some larger examples :