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junction n.  and  twin primes

First numbers that belong to both sets:

101, 103, 107, 109, 311, 313, 521, 1607, 1609, 1619, 1621, 2027, 2111, 2113, 2309, 2311, 2711, 2713, 3821, 3823, 4019, 4021, 4517, 4519, 4721, 4723, 5009, 5011, 5417, 5419, 7211, 7213, 9011, 9013, 9419, 9421, 9629, 9631, 10007, 10009, 11117, 11119, 11717, 11719, 12611, 12613, 12821, 12823, 13711, 13721, 13723, 14009, 14011, 14627, 16829, 16831, 17027, 17029, 17921, 17923, 20021, 20023, 20507, 20509, 20717, 20719, 21011, 21013, 21017, 21611, 21613, 22109, 22111, 23627, 24107, 24109, 24917, 24919, 25411, 26111, 26113, 26729, 26731, 28111, 29021, 29023, 30011, 30013, 31121, 31319, 31321, 31511, 31513, 31721, 31723, 31727, 32411, 32413, 32611, 34211, 34213, 35729, 35731, 36011, 36013, 37021, 41411, 41413, 41611, 42017, 42019, 44027, 44029, 45821, 45823, 47417, 47419, 48119, 48121, 48731, 48733, 50021, 50023, 51719, 51721, 53717, 53719, 54011, 54013, 54419, 54421, 54629, 54631, 55931, 55933, 57329, 57331, 57527, 57529, 58229, 58231, 60917, 60919, 62927, 62929, 63419, 63421, 64919, 64921, 67217, 67219, 67427, 67429, 69029, 69827, 69829, 70619, 70621, 71327, 72221, 72223, 72227, 76421, 76423, 76829, 76831, 81017, 81019, 82529, 82531, 82721, 82723, 82727, 82729, 83219, 83221, 84317, 84319, 84521, 84523, 85427, 85429, 85619, 85621, 85829, 85831, 86027, 86029, 86531, 86533, 86927, 86929, 87221, 87223, 87629, 87631, 90017, 90019, 90617, 90619, 90821, 90823, 91127, 92219, 92221, 96221, 96223, 96823, 98639, 99131, 99133, 99527, 99529, 101111, 101113, 101117, 101119, 102407, 102409, 105527, 106217, 106219, 106619, 106621, 107717, 107719, 108011, 108013, 109517, 109519, 110321, 110921, 110923, 111827, 112919, 112921, 113621, 113623, 115019, 115021, 116927, 116929, 117617, 117619, 119417, 119419, 121019, 121021, 122207, 122209, 122611, 124427, 125117, 125119, 125927, 125929, 126011, 126013, 126227, 127031, 127033, 128831, 128833, 129119, 129121, 129527, 129529, 131009, 131011, 132527, 134921, 134923, 135017, 135019, 135211, 140417, 140419, 140627, 141511, 143111.

Some larger examples :