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apocalyptic n.  and  emirp

First numbers that belong to both sets:

157, 937, 983, 1031, 1103, 1217, 1259, 1279, 1301, 1321, 1399, 1429, 1487, 1499, 1669, 1723, 1753, 1811, 1831, 1933, 1979, 3011, 3019, 3049, 3067, 3083, 3169, 3191, 3221, 3251, 3257, 3371, 3373, 3389, 3391, 3407, 3433, 3463, 3467, 3469, 3511, 3583, 3719, 3733, 3767, 3821, 3851, 3853, 3889, 3911, 3929, 7043, 7057, 7121, 7177, 7187, 7193, 7207, 7219, 7229, 7253, 7297, 7321, 7349, 7433, 7457, 7459, 7481, 7507, 7523, 7529, 7547, 7561, 7589, 7603, 7643, 7649, 7673, 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, 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, 10859, 10867, 10889, 10891, 10909, 10939, 10987, 10993, 11003, 11057, 11071, 11083, 11149, 11159, 11161, 11197, 11243, 11257, 11329, 11353, 11423, 11447, 11489, 11497, 11551, 11579, 11587, 11593, 11621, 11657, 11677, 11699, 11701, 11717, 11719, 11731, 11777, 11779, 11783, 11789, 11839, 11897, 11909, 11923, 11927, 11933, 11939, 11953, 11959, 11969, 11971, 11981, 12071, 12073, 12107, 12109, 12113, 12149, 12227, 12241, 12253, 12269, 12289, 12301, 12323, 12373, 12437, 12491, 12547, 12553, 12577, 12611, 12619, 12641, 12659, 12689, 12697, 12713, 12743, 12757, 12763, 12799, 12809, 12829, 12841, 12893, 12907, 12919, 12983, 13009, 13043, 13147, 13151, 13159, 13163, 13259, 13267, 13291, 13297, 13337, 13441, 13457, 13469, 13477, 13499, 13513, 13523, 13553, 13591, 13597.

Some larger examples :