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evil n.  and  palprime

First numbers that belong to both sets:

3, 5, 101, 353, 373, 383, 797, 11311, 12821, 13331, 14741, 17471, 18181, 19991, 30103, 30203, 30803, 31013, 34543, 34843, 35053, 35153, 35353, 35753, 38183, 38783, 39293, 70607, 71317, 72727, 73237, 73637, 75557, 78887, 79397, 79997, 90709, 93239, 93739, 94049, 94349, 94649, 94949, 95959, 96269, 96469, 97379, 97879, 98389, 1003001, 1043401, 1055501, 1074701, 1082801, 1085801, 1093901, 1126211, 1134311, 1145411, 1153511, 1163611, 1175711, 1183811, 1190911, 1201021, 1208021, 1215121, 1235321, 1242421, 1243421, 1250521, 1257521, 1268621, 1273721, 1276721, 1281821, 1286821, 1300031, 1303031, 1311131, 1317131, 1327231, 1343431, 1360631, 1371731, 1409041, 1411141, 1412141, 1437341, 1447441, 1456541, 1461641, 1496941, 1508051, 1513151, 1532351, 1548451, 1556551, 1557551, 1565651, 1594951, 1598951, 1609061, 1611161, 1616161, 1628261, 1633361, 1643461, 1646461, 1658561, 1684861, 1685861, 1712171, 1714171, 1737371, 1755571, 1777771, 1802081, 1824281, 1829281, 1831381, 1832381, 1842481, 1851581, 1878781, 1881881, 1883881, 1884881, 1903091, 1908091, 1909091, 1924291, 1936391, 1941491, 1951591, 1952591, 1957591, 1968691, 1987891, 1988891, 1993991, 1995991, 1998991, 3007003, 3026203, 3064603, 3073703, 3075703, 3083803, 3089803, 3091903, 3095903, 3103013, 3106013, 3127213, 3135313, 3140413, 3158513, 3196913, 3212123, 3222223, 3241423, 3245423, 3252523, 3258523, 3267623, 3272723, 3285823, 3288823, 3293923, 3304033, 3319133, 3331333, 3343433, 3353533, 3362633, 3364633, 3365633, 3392933, 3411143, 3417143, 3425243, 3427243, 3443443, 3449443, 3466643, 3470743, 3485843, 3503053, 3515153, 3517153, 3528253, 3553553, 3569653, 3589853, 3590953, 3591953, 3601063, 3618163, 3621263, 3627263, 3643463, 3670763, 3673763, 3680863, 3698963, 3708073, 3721273, 3763673, 3769673, 3773773, 3774773, 3784873, 3793973, 3804083, 3806083, 3814183, 3826283, 3829283, 3836383, 3842483, 3858583, 3863683, 3864683, 3869683, 3893983, 3899983, 3924293, 3938393, 3946493, 3964693, 3991993, 3994993, 7035307, 7036307, 7041407, 7057507, 7082807, 7087807, 7100017, 7115117, 7118117, 7134317, 7141417, 7145417, 7156517, 7159517, 7177717, 7194917, 7250527, 7256527, 7261627, 7267627, 7291927, 7300037, 7310137, 7347437, 7352537, 7354537, 7362637, 7365637, 7392937, 7401047, 7409047, 7415147, 7434347, 7461647, 7486847, 7489847, 7508057, 7527257, 7562657, 7564657, 7576757, 7592957, 7600067, 7611167, 7619167, 7622267, 7630367.

Some larger examples :