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apocalyptic n.  and  good prime

First numbers that belong to both sets:

251, 541, 929, 937, 1031, 1087, 1277, 1399, 1871, 1987, 2267, 2333, 2609, 2657, 2677, 2683, 2687, 3251, 3433, 3461, 3511, 3821, 3847, 3907, 3989, 4201, 4211, 4217, 4229, 4441, 4447, 4507, 4637, 4783, 4861, 4871, 4903, 4931, 4967, 5407, 5413, 5623, 5639, 5647, 5651, 6029, 6037, 6043, 6067, 6197, 6257, 6521, 6547, 6551, 6637, 6653, 6659, 6761, 6779, 6947, 7411, 7451, 7457, 7477, 7517, 7523, 7537, 8039, 8053, 8081, 8087, 8161, 8167, 8209, 8219, 8501, 8513, 8521, 8597, 8623, 8663, 8677, 8689, 8999, 9103, 9127, 9133, 9277, 9311, 9319, 9337, 9371, 9391, 9397, 9413, 9613, 10007, 10037, 10061, 10067, 10091, 10133, 10589, 10597, 10831, 10847, 11047, 11057, 11239, 11657, 11677, 11699, 11777, 11807, 11887, 11897, 12197, 12227, 12239, 12373, 12377, 12473, 12487, 12889, 13669, 13679, 13687, 14243, 14293, 14321, 14369, 14387, 14401, 14407, 14519, 14533, 14699, 14713, 15013, 15053, 15073, 15217, 15227, 15259, 15269, 16411, 16417, 16547, 16811, 16823, 16829, 16871, 16879, 16979, 17291, 17317, 17377, 17383, 17783, 17827, 17837, 17881, 17903, 17909, 18899, 18911, 19001, 19139, 19207, 19373, 19379, 19417, 19421, 19889, 19913, 19961, 20681, 20707, 20717, 20743, 20849, 20873, 20897, 20981, 21139, 21313, 21377, 21467, 21481, 21487, 21491, 21557, 22531, 22541, 22613, 22619, 22637, 22691, 22697, 22961, 23003, 23497, 23531, 23537, 23549, 23557, 23741, 24763, 24841, 24907, 24917, 25087, 25111, 25117, 25147, 25301, 25523, 25537, 25561, 25577, 25913, 26669, 26681, 27397, 27407, 27427, 27611, 27673, 27689, 27733, 27737, 28277, 28387, 28403, 28493, 28537, 28571, 28591, 28597, 29833, 29983.