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junction n.  and  prime n.

First numbers that belong to both sets:

101, 103, 107, 109, 113, 307, 311, 313, 317, 509, 521, 709, 719, 911, 919, 1009, 1013, 1213, 1217, 1409, 1607, 1609, 1613, 1619, 1621, 1811, 1823, 2017, 2027, 2111, 2113, 2309, 2311, 2521, 2711, 2713, 2719, 2917, 2927, 3011, 3209, 3217, 3221, 3407, 3413, 3613, 3617, 3623, 3821, 3823, 4019, 4021, 4027, 4111, 4513, 4517, 4519, 4523, 4721, 4723, 4919, 5009, 5011, 5209, 5413, 5417, 5419, 5623, 5813, 5821, 5827, 6029, 6113, 6121, 6311, 6317, 6323, 6521, 6719, 6917, 7013, 7019, 7211, 7213, 7219, 7411, 7417, 7621, 7817, 7823, 7829, 8111, 8117, 8123, 8311, 8317, 8513, 8521, 8527, 8719, 8731, 8923, 8929, 8933, 9011, 9013, 9221, 9227, 9413, 9419, 9421, 9619, 9623, 9629, 9631, 9817, 9829, 9833, 10007, 10009, 10211, 10607, 10613, 11027, 11113, 11117, 11119, 11311, 11317, 11321, 11519, 11717, 11719, 11923, 11927, 12007, 12011, 12211, 12409, 12413, 12421, 12611, 12613, 12619, 12821, 12823, 13109, 13121, 13309, 13313, 13513, 13523, 13711, 13721, 13723, 13913, 13921, 14009, 14011, 14207, 14221, 14411, 14419, 14423, 14621, 14627, 14813, 14821, 14827, 15017, 15031, 15107, 15121, 15313, 15319, 15511, 15527, 15727, 15919, 15923, 16007, 16217, 16223, 16411, 16417, 16421, 16427, 16619, 16823, 16829, 16831, 17021, 17027, 17029, 17033, 17117, 17123, 17317, 17321, 17327, 17519, 17729, 17921, 17923, 17929, 18013, 18211, 18217, 18223, 18413, 18427, 18617, 19031, 19121, 19319, 19531, 19717, 19727, 19919, 19927, 20021, 20023, 20107, 20113, 20117, 20507, 20509, 20521, 20717, 20719, 20921, 21011, 21013, 21017, 21211, 21221, 21407, 21419, 21611, 21613, 21617, 21817, 21821, 22027, 22109, 22111, 22307, 22511, 22717, 22721, 22727, 22921, 23011, 23017, 23209, 23417, 23623, 23627, 23813, 23819, 23827, 24019, 24023, 24029, 24107, 24109, 24113, 24121, 24317, 24517, 24527, 24917, 24919, 24923, 25013, 25219, 25411, 25423, 25621, 25819.

Some larger examples :