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junction n.  and  strong prime

First numbers that belong to both sets:

101, 107, 307, 311, 521, 719, 1009, 1213, 1607, 1619, 1823, 2027, 2111, 2309, 2521, 2711, 3011, 3217, 3407, 3613, 3821, 4019, 4513, 4517, 4721, 5009, 5413, 5417, 5623, 5821, 6029, 6113, 6311, 6521, 7013, 7211, 7411, 7817, 8111, 8311, 8513, 8521, 8731, 8923, 8929, 9011, 9221, 9413, 9419, 9619, 9629, 9829, 10007, 10211, 11027, 11113, 11117, 11311, 11317, 11519, 11717, 11923, 12007, 12409, 12611, 12821, 13121, 13309, 13513, 13721, 14009, 14419, 14621, 14627, 14813, 14821, 14827, 15121, 15527, 15727, 15919, 16217, 16411, 16417, 16823, 16829, 17021, 17027, 17117, 17317, 17729, 17921, 18211, 18427, 18617, 19031, 19121, 19531, 20021, 20113, 20507, 20717, 20921, 21011, 21017, 21211, 21221, 21611, 21817, 22027, 22109, 22717, 23011, 23017, 23417, 23623, 23627, 23813, 23827, 24019, 24107, 24317, 24527, 24917, 25013, 25219, 26111, 26317, 26729, 26921, 27011, 27427, 27817, 27823, 28027, 28723, 28921, 29017, 29021, 29221, 29423, 29629, 29819, 29833, 30011, 31121, 31307, 31319, 31511, 31721, 31727, 32411, 32423, 33023, 33107, 33311, 33521, 33713, 33923, 33931, 34019, 34211, 34421, 35023, 35311, 35323, 35521, 35527, 35729, 35923, 36011, 36629, 37117, 37529, 38219, 38431, 38629, 38821, 38833, 39719, 39727, 39929, 40519, 40927, 41011, 41213, 41221, 41411, 41617, 42017, 42323, 42719, 42923, 43013, 43223, 43427, 43627, 44027, 44111, 44119, 44729, 45427, 45631, 45817, 45821, 46021, 46327, 46723, 46919, 47417, 47431, 47623, 48119, 48523, 48731, 49429, 49627, 49823, 50021, 50207, 50221, 50411, 50627, 50821, 51031, 51109, 51511, 51517, 51713, 51719, 51929, 52009, 52021, 52223, 52627, 53113, 53323, 53717, 53917, 53923, 54011, 54419, 54617, 54629, 54829, 55313, 55529, 55717, 55921, 55927, 55931, 56417, 56431, 56629, 56821, 57037, 57329, 57527, 57727, 58013, 58027, 58229, 59119, 59333, 59723, 60029, 60317, 60521, 60719, 60727, 60917, 61211, 61223, 61627, 62119, 62323, 62723, 62921, 62927, 63419.

Some larger examples :