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congruent n.  and  palprime

First numbers that belong to both sets:

5, 7, 101, 151, 181, 191, 313, 353, 373, 383, 727, 757, 797, 919, 10301, 10501, 10601, 11311, 12421, 12821, 13831, 14341, 14741, 15551, 16061, 16661, 17471, 18181, 19391, 19991, 30103, 30703, 31013, 32423, 33533, 34543, 35053, 35353, 36263, 37573, 38183, 38783, 39293, 70207, 70607, 71317, 71917, 72727, 73037, 73237, 73637, 74047, 75557, 76367, 77477, 78487, 78887, 79397, 79997, 90709, 93239, 94349, 94649, 94949, 95959, 96269, 96469, 97879, 98389, 1035301, 1055501, 1074701, 1092901, 1093901, 1114111, 1117111, 1134311, 1150511, 1153511, 1175711, 1177711, 1178711, 1190911, 1193911, 1196911, 1201021, 1208021, 1221221, 1242421, 1243421, 1245421, 1262621, 1268621, 1280821, 1281821, 1286821, 1287821, 1300031, 1303031, 1327231, 1328231, 1343431, 1360631, 1362631, 1363631, 1411141, 1412141, 1437341, 1452541, 1456541, 1490941, 1496941, 1513151, 1532351, 1535351, 1550551, 1551551, 1556551, 1557551, 1572751, 1579751, 1594951, 1597951, 1598951, 1600061, 1609061, 1628261, 1640461, 1643461, 1646461, 1660661, 1684861, 1685861, 1688861, 1703071, 1707071, 1748471, 1761671, 1764671, 1831381, 1832381, 1851581, 1853581, 1856581, 1876781, 1878781, 1879781, 1895981, 1917191, 1930391, 1936391, 1951591, 1952591, 1957591, 1958591, 1970791, 1976791, 1993991, 1995991, 1998991, 3016103, 3072703, 3073703, 3075703, 3091903, 3095903, 3103013, 3106013, 3127213, 3140413, 3160613, 3166613, 3181813, 3187813, 3222223, 3223223, 3228223, 3241423, 3245423, 3260623, 3267623, 3283823, 3285823, 3286823, 3288823, 3310133, 3315133, 3319133, 3331333, 3337333, 3343433, 3353533, 3365633, 3391933, 3392933, 3411143, 3417143, 3439343, 3452543, 3470743, 3479743, 3503053, 3528253, 3541453, 3563653, 3569653, 3586853, 3589853, 3590953, 3601063, 3607063, 3621263, 3627263, 3643463, 3646463, 3680863, 3689863, 3716173, 3717173, 3732373, 3773773, 3774773, 3792973, 3793973, 3799973, 3812183, 3814183, 3836383, 3853583, 3858583, 3871783, 3878783, 3893983, 3899983, 3924293, 3927293, 3942493, 3946493, 3948493, 3964693, 3983893, 7041407, 7046407, 7065607, 7069607, 7082807, 7084807, 7087807, 7114117, 7115117, 7118117, 7134317, 7136317, 7155517, 7156517, 7158517, 7159517, 7177717, 7190917, 7194917, 7215127, 7250527, 7256527, 7257527, 7276727, 7278727, 7291927, 7300037, 7302037, 7324237, 7327237, 7347437, 7362637, 7365637, 7381837, 7388837, 7401047, 7403047, 7409047, 7461647.

Some larger examples :