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emirp  and  repunit

First numbers that belong to both sets:

13, 31, 73, 157, 1723, 3541, 19531, 35911, 37831, 95791, 117307, 121453, 123553, 158803, 171811, 307471, 322057, 346201, 704761, 731881, 735307, 766501, 922561, 939931, 975157, 987043, 1084723, 1135291, 1139557, 1145971, 1246573, 1398307, 1431613, 1441201, 1462891, 1492063, 1596433, 1619257, 1678321, 1735807, 1922383, 3134671, 3198733, 3263443, 3281533, 3292411, 3358057, 3416953, 3558883, 3592921, 3619507, 3730693, 3835261, 3882871, 3910507, 7271113, 7455631, 7521307, 9069133, 9165757, 9305551, 9569743, 9787513, 10378063, 10591771, 10696171, 10906507, 11192371, 11529421, 11611057, 11692981, 11720353, 12002761, 12127807, 12197557, 12207031, 12535141, 12791353, 13042933, 13151503, 13479913, 13931557, 14036263, 14330011, 14772493, 14996257, 15018571, 15089341, 15725191, 16228813, 16252993, 16970281, 17110633, 17610613, 17669413, 17846401, 17964883, 18024271, 18926851, 19022683, 19320421, 19417243, 19744693, 19771363, 19789153, 30409711, 30575371, 30674983, 30796951, 30830257, 31030471, 31298431, 31916851, 32450113, 33045253, 33843307, 34251757, 34886743, 35242033, 35420353, 35615581, 35754421, 36066031, 36078043, 36222343, 36766033, 37094191, 37155121, 37387111, 37423807, 38446201, 38831593, 39507511, 39999301, 70299841, 70350157, 71630833, 71834101, 72991393, 74433757, 74744671, 74969623, 75073561, 75959941, 76169257, 76781407, 76991851, 77484007, 90335521, 91021141, 91307581, 91766821, 91805143, 92092813, 92169601, 93035671, 93247993, 93557257, 94002721, 94468681, 94935793, 96108613, 96874807, 97039801, 97249183, 97525501, 97663807, 97960507, 98000101, 98376643, 99331123, 100230133, 100691191, 101858557, 102161557, 102201991, 102525751, 103235761, 104847361, 105380491, 106492081, 108941407, 111144307, 111397471, 114843373, 115982131, 116240743, 118407043, 118668343, 118711921, 119060833, 119847757, 120483553, 120945007, 121209091, 121473463, 121539601, 125765011, 127294807, 129083683, 130176691, 130519201, 130633471, 131618257, 132721921, 133252393, 133390951, 134571601, 135198757, 136130557, 136737943, 137018731, 141122521, 141621901, 146518921, 146688433, 147173293, 152386681, 156863101, 159201307, 159959257, 160440223, 161201113, 161429731, 162091093, 163469011, 166345507, 167870893, 168649183, 169143031, 169846057, 170158981, 170837971, 175761307, 176000023, 177489007, 178396093, 178476241, 178957507, 181023571, 181185061, 181427431, 181912657, 182236501, 182722807, 184837621, 185327383, 186472681, 187813321, 188060083, 189004141, 190012441, 190260643, 190785157, 192002593, 193279507, 193446373, 193613311, 194086693, 194253907, 195174871, 197557081, 198457657, 199162657.