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cyclic n.  and  emirp

First numbers that belong to both sets:

13, 17, 31, 37, 71, 73, 79, 97, 107, 113, 149, 157, 167, 179, 199, 311, 337, 347, 359, 389, 701, 709, 733, 739, 743, 751, 761, 769, 907, 937, 941, 953, 967, 971, 983, 991, 1009, 1021, 1031, 1033, 1061, 1069, 1091, 1097, 1103, 1109, 1151, 1153, 1181, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1279, 1283, 1301, 1321, 1381, 1399, 1409, 1429, 1439, 1453, 1471, 1487, 1499, 1511, 1523, 1559, 1583, 1597, 1601, 1619, 1657, 1669, 1723, 1733, 1741, 1753, 1789, 1811, 1831, 1847, 1867, 1879, 1901, 1913, 1933, 1949, 1979, 3011, 3019, 3023, 3049, 3067, 3083, 3089, 3109, 3121, 3163, 3169, 3191, 3203, 3221, 3251, 3257, 3271, 3299, 3301, 3319, 3343, 3347, 3359, 3371, 3373, 3389, 3391, 3407, 3433, 3463, 3467, 3469, 3511, 3527, 3541, 3571, 3583, 3613, 3643, 3697, 3719, 3733, 3767, 3803, 3821, 3851, 3853, 3889, 3911, 3917, 3929, 7027, 7043, 7057, 7121, 7177, 7187, 7193, 7207, 7219, 7229, 7253, 7297, 7321, 7349, 7433, 7457, 7459, 7481, 7507, 7523, 7529, 7547, 7561, 7577, 7589, 7603, 7643, 7649, 7673, 7681, 7687, 7699, 7717, 7757, 7817, 7841, 7867, 7879, 7901, 7927, 7949, 7951, 7963, 9001, 9011, 9013, 9029, 9041, 9103, 9127, 9133, 9161, 9173, 9209, 9221, 9227, 9241, 9257, 9293, 9341, 9349, 9403, 9421, 9437, 9439, 9467, 9479, 9491, 9497, 9521, 9533, 9547, 9551, 9601, 9613, 9643, 9661, 9679, 9721, 9749, 9769, 9781, 9787, 9791, 9803, 9833, 9857, 9871, 9883, 9923, 9931, 9941, 9967, 10007, 10009, 10039, 10061, 10067, 10069, 10079, 10091, 10151, 10159, 10177, 10247, 10253, 10273, 10321, 10333, 10343, 10391, 10429, 10453, 10457, 10459, 10487, 10499, 10613, 10639, 10651, 10711, 10739, 10781, 10853, 10859, 10867, 10889, 10891, 10909, 10939, 10987, 10993, 11003.

Some larger examples :