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prime n.  and  strobogrammatic n.

First numbers that belong to both sets:

11, 101, 181, 619, 16091, 18181, 19861, 61819, 116911, 119611, 160091, 169691, 191161, 196961, 686989, 688889, 1008001, 1068901, 1160911, 1180811, 1190611, 1191611, 1681891, 1690691, 1880881, 1881881, 1898681, 1908061, 1960961, 1990661, 6081809, 6100019, 6108019, 6110119, 6608099, 6610199, 6800089, 6801089, 6860989, 10069001, 10911601, 11069011, 11096011, 11869811, 11896811, 16069091, 16188191, 16811891, 16900691, 16969691, 16996691, 18611981, 18688981, 19188161, 19811861, 60088009, 60611909, 60800809, 61096019, 61669919, 61696919, 61969619, 66169199, 66896899, 66911699, 68669989, 68811889, 68969689, 69800869, 69911669, 100111001, 100609001, 100888001, 106101901, 108101801, 108619801, 109000601, 109609601, 109888601, 110111011, 111010111, 111181111, 111619111, 111689111, 116181911, 116916911, 118689811, 118818811, 118986811, 119888611, 119916611, 160080091, 160609091, 160689091, 161111191, 161619191, 161916191, 166080991, 166906991, 168101891, 169000691, 169609691, 180101081, 180986081, 181111181, 181888181, 186080981, 186619981, 188010881, 188619881, 188888881, 188906881, 189619681, 189689681, 189808681, 190000061, 190080061, 190689061, 191888161, 191916161, 196906961, 198010861, 198181861, 198818861, 199609661, 601818109, 601986109, 606916909, 608888809, 608916809, 609010609, 609080609, 609181609, 609818609, 610906019, 616111919, 616818919, 616906919, 618916819, 660916099, 661000199, 661609199, 666010999, 666080999, 666101999, 666619999, 668000899, 668609899, 681010189, 681986189, 686010989, 686181989, 688000889, 688689889, 688986889, 689010689, 689609689, 690181069, 691609169, 691689169, 696010969, 696080969, 696689969, 698000869, 698609869, 699916669, 1001961001, 1009696001, 1060110901, 1061001901, 1061881901, 1081691801, 1088698801, 1089886801, 1090000601, 1096699601, 1106009011, 1106889011, 1109006011, 1109696011, 1116119111, 1118698111, 1118968111, 1119886111, 1161881911, 1168008911, 1169886911, 1180690811, 1186119811, 1186969811, 1189006811, 1190880611, 1600000091, 1601961091, 1606699091, 1609966091, 1610000191, 1610960191, 1616699191, 1616969191, 1619696191, 1619966191, 1669116991, 1681961891, 1688008891, 1688968891, 1691691691, 1696699691, 1698118691, 1699966691, 1801691081, 1808968081, 1811961181, 1819116181, 1861001981, 1861111981, 1868008981, 1868698981, 1869886981, 1880690881, 1886969881, 1888698881, 1901691061, 1901881061, 1906699061, 1908118061, 1909006061, 1909966061, 1910880161, 1919966161, 1968118961, 1969006961, 1980110861, 1980880861, 1981111861, 1989116861, 1989886861, 6000110009, 6009886009, 6010000109, 6016969109, 6018118109, 6061001909, 6061961909, 6068008909, 6080000809, 6089006809, 6100110019, 6100690019, 6110880119, 6160110919, 6166009919, 6180880819, 6181111819, 6188008819, 6189886819, 6190690619, 6196009619, 6601691099, 6606119099, 6606889099, 6609886099, 6616119199, 6661691999, 6668008999, 6668698999, 6669886999, 6688698899, 6689006899, 6689886899, 6691961699, 6698888699, 6801111089, 6806699089, 6808008089, 6811001189, 6818008189, 6818698189, 6819886189, 6860690989.

Some larger examples :