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emirpimes  and  junction n.

First numbers that belong to both sets:

115, 319, 511, 622, 723, 913, 921, 923, 1011, 1211, 1219, 1306, 1318, 1405, 1411, 1415, 1417, 1514, 1623, 1714, 1817, 2021, 2206, 2614, 2818, 3007, 3013, 3106, 3207, 3215, 3415, 3419, 3421, 3518, 3817, 4109, 4115, 4117, 4121, 4307, 4309, 4313, 4319, 4321, 4511, 4711, 4727, 5114, 5314, 5318, 5411, 5611, 5615, 5617, 5627, 5914, 5926, 6031, 6418, 6614, 7114, 7223, 7318, 7419, 7421, 7423, 7522, 7617, 7619, 7629, 7831, 8321, 9026, 9034, 9122, 9326, 9427, 9518, 9617, 9627, 9722, 9827, 9934, 10003, 10027, 10033, 10213, 10217, 10219, 10306, 10405, 10411, 10417, 10623, 10817, 11006, 11013, 11015, 11103, 11309, 11422, 11723, 11917, 12003, 12013, 12106, 12209, 12217, 12407, 12419, 12718, 12813, 13017, 13021, 13117, 13307, 13315, 13418, 13511, 13517, 13521, 13814, 13917, 13929, 14005, 14015, 14017, 14019, 14026, 14213, 14219, 14318, 14417, 14611, 14617, 14623, 14815, 14918, 15019, 15109, 15721, 15927, 15931, 16009, 16013, 16018, 16019, 16021, 16022, 16118, 16213, 16322, 16413, 16526, 16613, 16615, 16621, 17023, 17218, 17311, 17315, 17414, 17426, 17513, 17517, 17521, 17527, 17614, 17717, 18021, 18022, 18023, 18215, 18219, 18227, 18514, 18619, 18623, 18823, 18827, 18829, 18833, 19021, 19029, 19127, 19226, 19315, 19517, 19529, 19731, 19921, 19931, 19933, 20311, 20321, 20711, 20917, 20927, 22006, 22115, 22309, 22313, 22513, 22711, 22723, 24014, 24031, 24313, 24515, 24929, 24931, 26018, 26933, 28117, 28121, 28214, 28327, 28531, 28931, 30019, 30021, 30027, 30407, 30413, 30417, 30421, 30518, 30611, 30619, 30722, 30813, 30827, 30922, 31015, 31021, 31029, 31105, 31107, 31109, 31826, 31917, 31919, 31921, 31927, 32209, 32217, 32221, 32722, 32815, 33017, 33109, 33121, 33515, 33622, 33717, 33729, 33919, 34007, 34009, 34223, 34415, 34619, 34621, 34718, 34829, 34831, 35018, 35021, 35218, 35513, 35515, 35614, 35723, 35727, 36019, 36021, 36026, 36122, 36227, 36413.

Some larger examples :