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bemirp  and  prime n.

First numbers that belong to both sets:

1061, 1091, 1601, 1901, 10061, 10091, 16001, 19001, 106861, 109891, 168601, 198901, 1106881, 1109881, 1606081, 1806061, 1809091, 1886011, 1889011, 1909081, 10806881, 10809881, 11061811, 11091811, 11609681, 11698691, 11816011, 11819011, 11906981, 11968961, 16061681, 16098661, 16166681, 16689061, 16880681, 16986911, 18608861, 18616061, 18616681, 18661681, 18666161, 18690611, 18860801, 18890801, 18908891, 18919091, 18919981, 18960911, 18991981, 18999191, 19068991, 19091981, 19199981, 19689611, 19880981, 19986091, 100688611, 100988911, 101060111, 101090111, 106061611, 106186681, 106198601, 106199801, 106888891, 106890011, 106891601, 106968691, 106996801, 108016891, 108019861, 108160081, 108190081, 108661901, 108661981, 108699601, 108966901, 108991601, 108991681, 109091911, 109166801, 109168901, 109189981, 109669801, 109698961, 109860011, 109861901, 109888861, 110068901, 110098601, 110600981, 110900681, 111060101, 111090101, 116088811, 116160601, 116686811, 116886001, 116898961, 116969891, 116999161, 118080161, 118080191, 118618891, 118686611, 118880611, 118880911, 118918861, 118989911, 119088811, 119190901, 119666191, 119696861, 119868691, 119889001, 119989811, 160008661, 160800881, 160980991, 161080811, 161188681, 161668961, 161899861, 161999611, 166086091, 166106981, 166168861, 166180081, 166800061, 166980881, 168668881, 168696911, 168819811, 168861661, 168888901, 168910801, 168998161, 169806181, 169866161, 169896901, 169898611, 180061801, 180081661, 180081991, 180091801, 181608961, 181908691, 186009011, 186199801, 186681601, 186881161, 186901991, 188008061, 188008091, 188086991, 188089661, 188866861, 188899891, 189006011, 189166801, 189601661, 189881191, 189981901, 190008991, 190680661, 190800881, 191080811, 191188981, 191666911, 191866891, 191998691, 196809181, 196868911, 196869601, 196899191, 198610801, 198668191, 198816811, 198888601, 198891991, 198969611, 198998881, 199089061, 199109681, 199180081, 199198891, 199680881, 199800091, 1006088861, 1006606801, 1006919981, 1006986881, 1006986991, 1008688981, 1008816181, 1008819181, 1008988681, 1009088891, 1009616681, 1009689661, 1009689881, 1009909801, 1010601181, 1010886661, 1010889991, 1010901181, 1016011991, 1016118011, 1016880191, 1016910161, 1019011661, 1019118011, 1019610191, 1019880161, 1060116901, 1060900081, 1061069861, 1061900911, 1061989601, 1069010011, 1069110901, 1069119991, 1069669661, 1069891601, 1069916891, 1069981111, 1080068911, 1080098611, 1080860861, 1080890891, 1081169681, 1081196981, 1086066001, 1086916091, 1088068181, 1088098181, 1088600911, 1088900611, 1089099001, 1089619061, 1090119601, 1090600081, 1091096891, 1091600611, 1091686901, 1096010011, 1096110601, 1096116661, 1096619861, 1096681111, 1096861901, 1096996991, 1100106901, 1100109601, 1101186161, 1101189191, 1106089891, 1108116101, 1108119101, 1109086861, 1110010661, 1110010991, 1110606181, 1110909181, 1111866901, 1111899601, 1116001961, 1116119891, 1118066681, 1118099981, 1119001691, 1119116861, 1160010191, 1160061901, 1160098801, 1160816161, 1160896081, 1160919691, 1161110191, 1161111661.

Some larger examples :