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congruent n.  and  good prime

First numbers that belong to both sets:

5, 29, 37, 41, 53, 71, 101, 127, 149, 191, 223, 257, 269, 311, 431, 541, 557, 599, 727, 733, 821, 853, 967, 1031, 1087, 1151, 1213, 1277, 1367, 1399, 1423, 1543, 1597, 1847, 1861, 1871, 1973, 1997, 2063, 2237, 2333, 2647, 2677, 2687, 2999, 3167, 3433, 3461, 3511, 3527, 3821, 3847, 3989, 4229, 4441, 4447, 4481, 4621, 4637, 4783, 4861, 4871, 4903, 4967, 5381, 5407, 5413, 5623, 5639, 5647, 6007, 6029, 6037, 6197, 6263, 6551, 6637, 6653, 6823, 7477, 7517, 8039, 8053, 8087, 8167, 8501, 8521, 8597, 8623, 8663, 8677, 8999, 9103, 9127, 9133, 9151, 9277, 9311, 9319, 9391, 9397, 9413, 9613, 10007, 10037, 10061, 10133, 10589, 10597, 10831, 10847, 10853, 11047, 11239, 11677, 11807, 11887, 12197, 12239, 12373, 12487, 12889, 13669, 13679, 13687, 14293, 14321, 14407, 14519, 14533, 15013, 15053, 15073, 15269, 16417, 16823, 16829, 16871, 16879, 17317, 17383, 17783, 17837, 17903, 17909, 18911, 19207, 19373, 19421, 20717, 20743, 20981, 21487, 21557, 22541, 22613, 22637, 23497, 23549, 23557, 23741, 24917, 25087, 25111, 25117, 25301, 25577, 26669, 26681, 27397, 27407, 27733, 28277, 28493, 28591, 28597, 29983, 30631, 30637, 30671, 30757, 31957, 33287, 33311, 35797, 35831, 35951, 36527, 36671, 38149, 38167, 38543, 38557, 38669, 39079, 40423, 40471, 40693, 40751, 40759, 40813, 41039, 41141, 41879, 41887, 41941, 43573, 43933, 43943, 43961, 44449, 45943, 46021, 46133, 46141, 46399, 46439, 47087, 47111, 47119, 47269, 47279, 47287, 47293, 48311, 48397, 48407, 48463, 48479, 48751, 48757, 48973, 48989, 49103, 50741, 50767, 50821, 51109, 51197, 51341, 51407, 51413, 52501, 52511, 52541, 53591, 54269, 54311, 54319, 54367, 55661, 56359, 56377, 56431, 56437, 60589, 60607, 61253, 61463, 61469, 63277, 63311, 64567, 64849, 64871, 64877, 64997, 65089, 65407, 65519, 66293, 66343, 66359, 66919, 69653, 69677, 69821, 69991, 69997, 70111.

Some larger examples :