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strong prime  and  twin primes

First numbers that belong to both sets:

11, 17, 29, 41, 59, 71, 101, 107, 137, 149, 179, 191, 197, 227, 239, 269, 281, 311, 347, 419, 431, 461, 521, 569, 599, 617, 641, 659, 809, 821, 827, 857, 881, 1019, 1031, 1049, 1061, 1091, 1151, 1229, 1277, 1289, 1301, 1319, 1427, 1451, 1481, 1487, 1607, 1619, 1667, 1697, 1721, 1787, 1871, 1877, 1931, 1949, 1997, 2027, 2081, 2087, 2111, 2129, 2141, 2237, 2267, 2309, 2339, 2381, 2549, 2591, 2657, 2687, 2711, 2729, 2789, 2801, 2969, 2999, 3119, 3167, 3251, 3257, 3299, 3329, 3359, 3371, 3389, 3461, 3467, 3527, 3539, 3557, 3581, 3671, 3767, 3821, 3851, 3917, 3929, 4001, 4019, 4049, 4091, 4127, 4157, 4217, 4229, 4241, 4259, 4271, 4337, 4421, 4481, 4517, 4547, 4637, 4649, 4721, 4787, 4799, 4931, 4967, 5009, 5021, 5099, 5231, 5279, 5417, 5441, 5477, 5501, 5519, 5639, 5651, 5657, 5741, 5849, 5867, 5879, 6089, 6131, 6197, 6269, 6299, 6359, 6449, 6551, 6569, 6659, 6689, 6701, 6761, 6779, 6791, 6827, 6869, 6947, 6959, 7127, 7211, 7307, 7331, 7349, 7457, 7487, 7547, 7559, 7589, 7757, 7877, 7949, 8009, 8087, 8219, 8231, 8291, 8387, 8429, 8537, 8597, 8627, 8819, 8837, 8861, 8969, 8999, 9011, 9041, 9239, 9281, 9341, 9419, 9431, 9437, 9461, 9629, 9677, 9719, 9767, 9857, 9929, 10007, 10037, 10067, 10091, 10139, 10271, 10301, 10331, 10427, 10457, 10499, 10529, 10709, 10859, 10889, 10937, 11057, 11069, 11117, 11159, 11171, 11351, 11489, 11549, 11699, 11717, 11777, 11831, 11939, 11969, 12041, 12071, 12107, 12161, 12239, 12251, 12377, 12539, 12611, 12821, 12917, 13001, 13007, 13217, 13337, 13397, 13679, 13691, 13709, 13721, 13757, 13829, 13877, 13901, 13931, 13997, 14009, 14081, 14249, 14321, 14387, 14447, 14549, 14561, 14591, 14627, 14867, 15137, 15269, 15287, 15329, 15359, 15581, 15641, 15647, 15731, 15737.

Some larger examples :