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congruent n.  and  weak prime

First numbers that belong to both sets:

7, 13, 23, 31, 47, 61, 103, 109, 151, 167, 181, 199, 229, 271, 293, 313, 317, 349, 353, 359, 383, 389, 421, 463, 503, 509, 647, 661, 677, 709, 743, 761, 773, 797, 823, 829, 839, 863, 887, 911, 919, 941, 983, 997, 1013, 1021, 1039, 1063, 1069, 1093, 1109, 1201, 1217, 1231, 1237, 1279, 1303, 1321, 1327, 1373, 1381, 1429, 1439, 1453, 1493, 1559, 1583, 1613, 1621, 1637, 1669, 1709, 1759, 1789, 1831, 1879, 1933, 1951, 1999, 2029, 2039, 2069, 2113, 2143, 2207, 2213, 2221, 2239, 2269, 2273, 2311, 2341, 2351, 2357, 2383, 2399, 2423, 2447, 2477, 2543, 2551, 2557, 2621, 2663, 2693, 2719, 2777, 2791, 2837, 2861, 2887, 2909, 2917, 2927, 2957, 3001, 3023, 3191, 3221, 3229, 3253, 3271, 3301, 3373, 3391, 3413, 3463, 3469, 3517, 3533, 3541, 3559, 3583, 3593, 3623, 3677, 3701, 3709, 3797, 3823, 3853, 3863, 3881, 3911, 3919, 3967, 4007, 4021, 4079, 4093, 4111, 4133, 4159, 4231, 4261, 4373, 4397, 4423, 4463, 4493, 4519, 4549, 4567, 4639, 4663, 4679, 4703, 4733, 4759, 4789, 4793, 4831, 4877, 4889, 4909, 4919, 4933, 4943, 4957, 4973, 5023, 5087, 5101, 5119, 5197, 5237, 5309, 5333, 5351, 5399, 5449, 5479, 5503, 5573, 5581, 5591, 5653, 5669, 5693, 5701, 5717, 5743, 5749, 5783, 5791, 5813, 5861, 5869, 5903, 5927, 6047, 6053, 6079, 6101, 6133, 6151, 6173, 6199, 6221, 6229, 6271, 6277, 6287, 6301, 6343, 6397, 6529, 6581, 6607, 6661, 6679, 6703, 6709, 6719, 6781, 6829, 6871, 6911, 6917, 6949, 6983, 7001, 7079, 7109, 7159, 7213, 7247, 7253, 7309, 7333, 7351, 7417, 7541, 7549, 7561, 7591, 7607, 7621, 7703, 7727, 7759, 7793, 7829, 7853, 7879, 7951, 8069, 8093, 8101, 8191, 8221, 8237, 8293, 8317, 8389, 8423, 8431, 8447, 8527, 8543.

Some larger examples :