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interprime n.  and  modest n.

First numbers that belong to both sets:

26, 39, 69, 111, 266, 309, 399, 436, 515, 618, 822, 933, 1003, 1011, 1066, 1254, 1299, 1527, 1599, 1624, 1827, 1854, 2022, 2066, 2444, 2799, 2933, 3045, 3055, 3081, 3099, 3399, 3699, 4054, 4266, 4444, 4555, 4866, 5045, 5055, 5481, 6009, 6090, 6266, 6293, 6333, 6999, 7063, 8088, 8666, 10074, 10101, 11037, 12108, 12111, 12162, 12444, 14042, 14054, 14378, 15555, 17037, 18027, 18054, 18666, 20022, 20148, 20180, 21027, 21189, 22297, 22814, 24036, 24074, 24108, 24111, 24333, 25925, 27037, 27333, 27999, 28054, 28063, 28084, 28666, 28756, 30090, 30111, 30135, 30270, 30555, 30666, 32054, 32108, 33099, 33891, 35135, 35333, 36108, 36486, 38342, 38703, 39351, 39999, 40011, 40022, 40090, 40222, 40666, 41369, 42222, 44814, 45333, 45555, 47999, 48144, 48648, 49063, 50090, 50150, 50370, 50450, 52054, 54111, 56084, 57703, 60033, 60090, 60324, 60405, 62727, 63777, 64074, 65135, 66297, 69999, 70105, 70303, 70518, 72216, 72222, 72648, 72666, 75081, 75225, 75333, 75405, 75555, 75999, 76222, 78111, 78702, 80144, 80148, 83999, 84222, 84333, 84666, 84756, 85153, 90027, 90081, 90222, 90243, 90333, 90405, 90909, 92148, 93333, 94282, 95333, 95555, 96162, 96216, 96222, 96999, 98126, 98666, 99891, 100011, 100225, 102333, 103111, 104148, 106666, 110101, 110666, 112444, 112504, 114666, 114999, 115851, 120044, 120216, 120296, 120360, 120666, 120999, 123999, 124222, 126162, 126378, 126567, 128333, 128666, 133703, 134603, 135729, 136306, 138999, 140063, 140202, 141999, 143407, 144162, 144888, 145185, 150222, 150555, 150999, 152216, 152888, 153999, 154297, 156222, 156324, 160176, 160370, 160432, 160666, 162729, 165495, 169333, 170370, 174261, 174666, 176407, 176594, 176814, 178534, 180033, 180324, 180540, 180555, 180740, 181543, 181782, 182481, 184276, 184444, 184851, 185454, 187999, 190057, 192576, 192888, 196259, 198222, 198666, 198814, 200006, 200165, 200180, 200360, 200404, 201333, 201626, 201999, 202333, 204306, 204324, 205333, 206060, 207999, 208962, 209999, 210099, 210189, 210231, 210270.

Some larger examples :