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apocalyptic n.  and  weak prime

First numbers that belong to both sets:

443, 647, 823, 859, 983, 1217, 1259, 1279, 1303, 1321, 1429, 1483, 1493, 1499, 1627, 1669, 1723, 1811, 1831, 1889, 1933, 1979, 2039, 2069, 2083, 2099, 2113, 2131, 2143, 2161, 2239, 2243, 2251, 2269, 2273, 2311, 2351, 2383, 2399, 2447, 2477, 2543, 2551, 2557, 2593, 2659, 2699, 2791, 2837, 2843, 2861, 2887, 2909, 2927, 2939, 2957, 2971, 3001, 3041, 3049, 3067, 3083, 3137, 3169, 3191, 3221, 3229, 3253, 3323, 3331, 3373, 3391, 3463, 3469, 3533, 3559, 3583, 3617, 3623, 3673, 3677, 3709, 3739, 3797, 3853, 3889, 3911, 3919, 3923, 3947, 3967, 4021, 4027, 4051, 4057, 4079, 4093, 4099, 4159, 4219, 4231, 4261, 4273, 4289, 4339, 4363, 4423, 4451, 4463, 4493, 4519, 4523, 4549, 4567, 4643, 4651, 4663, 4679, 4733, 4759, 4789, 4793, 4801, 4877, 4889, 4909, 4933, 4937, 4957, 4969, 4973, 5059, 5081, 5087, 5119, 5153, 5171, 5179, 5197, 5209, 5233, 5237, 5309, 5333, 5351, 5399, 5419, 5443, 5449, 5479, 5483, 5503, 5507, 5521, 5531, 5573, 5581, 5591, 5641, 5653, 5659, 5669, 5693, 5717, 5743, 5749, 5783, 5813, 5843, 5851, 5881, 5939, 5953, 5987, 6011, 6047, 6053, 6079, 6091, 6101, 6121, 6133, 6151, 6173, 6199, 6221, 6271, 6277, 6287, 6301, 6329, 6343, 6361, 6397, 6451, 6481, 6491, 6529, 6553, 6571, 6581, 6607, 6619, 6661, 6691, 6703, 6709, 6737, 6781, 6793, 6803, 6829, 6833, 6841, 6871, 6883, 6917, 6949, 6961, 6971, 6983, 7001, 7019, 7043, 7129, 7159, 7193, 7213, 7219, 7247, 7253, 7309, 7333, 7351, 7369, 7417, 7433, 7459, 7481, 7489, 7507, 7529, 7541, 7561, 7591, 7607, 7621, 7643, 7649, 7673, 7691, 7703, 7727, 7759, 7793, 7829, 7853, 7879, 7883, 7907, 7937, 7951, 7963, 8011, 8017, 8059, 8069, 8089, 8093, 8101, 8123, 8171, 8179, 8191, 8221, 8233, 8237, 8243, 8273, 8293.

Some larger examples :