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strong prime  and  weakly prime

First numbers that belong to both sets:

505447, 584141, 604171, 1062599, 5152507, 5564453, 5575259, 6173731, 6236179, 6463267, 7204777, 7469789, 7858771, 8353427, 8532761, 8639089, 9016079, 9608189, 9931447, 10564877, 11124403, 11593019, 12325739, 14075273, 14090887, 17412427, 17412599, 18561293, 18953677, 21044557, 21281479, 22138349, 22480351, 23228479, 25081361, 25151927, 25475617, 25556941, 25872199, 27242179, 27425521, 28070047, 29348797, 30791767, 31240481, 34302127, 34349969, 35009671, 35319367, 35673679, 36221597, 37095427, 39397009, 39724417, 40085977, 40432489, 40638727, 40812781, 42145837, 42758917, 43414669, 43988459, 46301219, 46448719, 46591507, 47263001, 47457367, 47744239, 48024359, 48143047, 48341959, 48384977, 49453847, 50170513, 50456519, 50592911, 51340909, 52127189, 53355689, 53454589, 53753587, 55959643, 56485057, 56743469, 57177889, 59160317, 61575539, 61589579, 64843237, 65029997, 65314439, 66117679, 66640253, 67959743, 68030449, 68428379, 68495347, 68970457, 69374167, 70006253, 70514141, 70850641, 71756029, 71760109, 72168857, 72418187, 72422393, 72504457, 72760297, 73022273, 73440439, 74543663, 74711779, 75374149, 75448801, 76720291, 77511487, 77675639, 77844287, 78562307, 81397777, 81608981, 82319411, 82764371, 82817039, 82892633, 82905047, 83407327, 84159917, 84255251, 84487439, 84733919, 85415249, 86504879, 86688269, 88826693, 88903379, 89146619, 89473777, 89602771, 90997241, 92027977, 92519951, 94113781, 94912583, 95401417, 95517517, 95663761, 97069493, 97353379, 97792117, 97864961, 98701003, 98954621, 99041179, 99157987, 99595919.