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aban n.  and  twin primes

First numbers that belong to both sets:

3, 5, 7, 11, 13, 17, 19, 29, 31, 41, 43, 59, 61, 71, 73, 101, 103, 107, 109, 137, 139, 149, 151, 179, 181, 191, 193, 197, 199, 227, 229, 239, 241, 269, 271, 281, 283, 311, 313, 347, 349, 419, 421, 431, 433, 461, 463, 521, 523, 569, 571, 599, 601, 617, 619, 641, 643, 659, 661, 809, 811, 821, 823, 827, 829, 857, 859, 881, 883, 1000037, 1000039, 1000211, 1000213, 1000289, 1000291, 1000427, 1000429, 1000577, 1000579, 1000619, 1000621, 1000667, 1000669, 1000721, 1000723, 1000847, 1000849, 1000859, 1000861, 1000919, 1000921, 2000081, 2000083, 2000291, 2000293, 2000351, 2000353, 2000387, 2000389, 2000519, 2000521, 2000939, 2000941, 3000131, 3000133, 3000299, 3000301, 3000377, 3000379, 3000539, 3000541, 3000929, 3000931, 4000037, 4000039, 4000079, 4000081, 4000301, 4000303, 4000541, 4000543, 4000649, 4000651, 4000691, 4000693, 4000937, 4000939, 4000949, 4000951, 5000111, 5000113, 5000549, 5000551, 5000687, 5000689, 5000759, 5000761, 5000927, 5000929, 6000101, 6000103, 6000119, 6000121, 6000479, 6000481, 6000569, 6000571, 6000821, 6000823, 6000857, 6000859, 7000127, 7000129, 7000517, 7000519, 7000661, 7000663, 8000051, 8000053, 8000099, 8000101, 8000117, 8000119, 8000171, 8000173, 8000219, 8000221, 8000357, 8000359, 8000411, 8000413, 8000609, 8000611, 8000747, 8000749, 8000789, 8000791, 8000807, 8000809, 8000891, 8000893, 8000981, 8000983, 9000377, 9000379, 9000779, 9000781, 9000791, 9000793, 9000839, 9000841, 10000139, 10000141, 10000451, 10000453, 10000721, 10000723, 10000871, 10000873, 11000081, 11000083, 11000111, 11000113, 11000291, 11000293, 11000399, 11000401, 11000747, 11000749, 12000257, 12000259, 12000269, 12000271, 12000407, 12000409, 12000431, 12000433, 12000509, 12000511, 12000881, 12000883, 12000977, 12000979, 13000217, 13000219, 13000301, 13000303, 13000331, 13000333, 13000751, 13000753, 13000829, 13000831, 14000087, 14000089, 14000339, 14000341, 14000507, 14000509, 14000711, 14000713, 15000521, 15000523, 15000779, 15000781, 15000911, 15000913, 16000079, 16000081, 16000667, 16000669, 16000877, 16000879, 16000979, 16000981, 17000441, 17000443, 17000957, 17000959, 18000137, 18000139, 18000347, 18000349, 18000401, 18000403, 18000767, 18000769, 18000887, 18000889, 18000947, 18000949, 19000409, 19000411, 19000517, 19000519, 19000559, 19000561, 19000979, 19000981, 20000159.

Some larger examples :