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balanced prime  and  palindromic n.

First numbers that belong to both sets:

5, 373, 11411, 30103, 34543, 35753, 38183, 1145411, 1190911, 1335331, 1338331, 1579751, 1643461, 3283823, 3621263, 3627263, 3670763, 3698963, 3812183, 3931393, 7215127, 7690967, 7722277, 7867687, 9351539, 9602069, 9604069, 9732379, 9820289, 9932399, 103363301, 105575501, 107858701, 107949701, 120434021, 124525421, 126424621, 126727621, 127747721, 130020031, 130636031, 137171731, 138989831, 140777041, 149333941, 150272051, 151585151, 151777151, 152505251, 152565251, 152696251, 156434651, 156757651, 156848651, 158696851, 160696061, 161484161, 162232261, 164696461, 165808561, 169555961, 172060271, 176373671, 176646671, 178747871, 179060971, 183232381, 187090781, 189292981, 191171191, 191595191, 193191391, 193212391, 194303491, 197868791, 199363991, 300656003, 303616303, 304131403, 306323603, 307404703, 308898803, 310636013, 310969013, 313111313, 314646413, 316141613, 316696613, 319797913, 322474223, 325060523, 328828823, 329282923, 329787923, 332121233, 332484233, 333212333, 334414433, 337939733, 342797243, 344757443, 346777643, 347444743, 350828053, 352909253, 354515453, 354767453, 356010653, 362474263, 363595363, 366040663, 368969863, 369343963, 369515963, 375232573, 376494673, 395616593, 397909793, 700717007, 701595107, 702767207, 704070407, 707222707, 710030017, 711131117, 711535117, 716232617, 717646717, 718777817, 720262027, 726797627, 729202927, 730737037, 732494237, 736969637, 740999047, 741424147, 745363547, 754747457, 759727957, 771868177, 775101577, 782696287, 784161487, 791969197, 798212897, 798818897, 902585209, 905696509, 915161519, 915313519, 919686919, 934525439, 936181639, 941828149, 943272349, 952767259, 964282469, 970717079, 972626279, 974757479, 975626579, 980111089, 985212589, 987101789, 989565989, 990353099, 994848499, 996989699.