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congruent n.  and  emirp

First numbers that belong to both sets:

13, 31, 37, 71, 79, 149, 157, 167, 199, 311, 359, 389, 701, 709, 733, 743, 751, 761, 941, 967, 983, 991, 1021, 1031, 1061, 1069, 1103, 1109, 1151, 1181, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1279, 1301, 1321, 1381, 1399, 1429, 1439, 1453, 1471, 1487, 1511, 1559, 1583, 1597, 1669, 1733, 1741, 1789, 1831, 1847, 1879, 1901, 1933, 1949, 3023, 3109, 3191, 3221, 3271, 3301, 3319, 3343, 3359, 3373, 3389, 3391, 3407, 3433, 3463, 3469, 3511, 3527, 3541, 3583, 3613, 3719, 3733, 3767, 3821, 3853, 3911, 3917, 7207, 7229, 7253, 7321, 7349, 7561, 7589, 7687, 7717, 7757, 7879, 7901, 7927, 7949, 7951, 9013, 9029, 9103, 9127, 9133, 9173, 9221, 9257, 9293, 9341, 9349, 9421, 9437, 9439, 9479, 9497, 9521, 9533, 9551, 9601, 9613, 9661, 9679, 9749, 9781, 9791, 9871, 9941, 9967, 10007, 10039, 10061, 10069, 10079, 10151, 10159, 10247, 10253, 10333, 10343, 10391, 10429, 10453, 10487, 10613, 10639, 10711, 10781, 10853, 10909, 11071, 11149, 11159, 11197, 11423, 11447, 11551, 11621, 11677, 11701, 11717, 11719, 11783, 11789, 11839, 11903, 11909, 11927, 11933, 11959, 11981, 12071, 12109, 12119, 12149, 12241, 12253, 12269, 12301, 12373, 12437, 12743, 12757, 12799, 12809, 12829, 12893, 12919, 12983, 13151, 13159, 13441, 13469, 13477, 13513, 13591, 13597, 13693, 13709, 13711, 13751, 13757, 13759, 13781, 13789, 13829, 13841, 13903, 13933, 14029, 14071, 14087, 14143, 14207, 14221, 14293, 14303, 14327, 14423, 14431, 14447, 14449, 14479, 14519, 14549, 14551, 14557, 14591, 14593, 14621, 14629, 14717, 14821, 14831, 14879, 14929, 14957, 15013, 15053, 15101, 15149, 15263, 15349, 15383, 15461, 15493, 15511, 15527, 15541, 15661, 15679, 15733, 15737, 15791, 15919, 15973, 16007, 16063, 16103, 16111, 16127, 16223, 16453, 16493, 16567, 16573, 16829, 16879, 16943, 17021, 17047, 17117, 17207, 17383, 17477.

Some larger examples :