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modest n.  and  unprimeable n.

First numbers that belong to both sets:

206, 515, 622, 844, 1266, 1418, 1466, 1644, 1648, 1672, 1688, 1854, 2044, 2045, 2074, 2488, 3054, 3055, 3090, 3236, 3244, 3248, 3266, 3288, 3666, 4036, 4060, 4066, 4088, 4108, 4148, 4555, 4854, 5045, 5066, 5135, 5466, 5672, 7090, 8024, 8072, 8074, 10015, 10018, 10045, 10054, 10370, 12054, 12444, 12666, 14042, 14126, 14378, 15045, 16018, 16024, 16048, 16296, 16592, 20006, 20030, 20036, 20090, 20135, 20198, 20222, 20270, 20370, 20606, 22594, 24036, 24054, 24148, 24216, 24296, 24648, 24666, 25045, 25135, 25555, 25925, 26074, 26078, 26962, 28042, 28074, 28148, 28252, 28378, 30370, 32036, 32048, 32108, 32222, 32288, 32432, 32592, 32666, 34074, 34102, 34222, 35045, 35135, 35185, 35555, 35945, 36054, 36148, 36324, 36444, 36486, 36666, 38074, 38222, 38342, 40022, 40044, 40045, 40054, 40072, 40074, 40108, 40132, 40135, 40148, 40202, 40222, 40296, 40370, 40396, 40404, 40444, 40666, 40740, 42054, 42126, 42518, 44066, 44148, 44198, 44396, 44594, 44666, 48054, 48144, 48148, 48216, 48324, 50015, 50165, 50185, 50666, 52074, 52078, 52444, 52468, 54074, 54222, 54486, 55135, 55185, 55495, 55555, 56072, 56074, 56216, 56222, 56252, 56756, 56888, 58522, 60054, 60066, 60180, 60185, 60198, 60324, 60405, 60540, 60555, 60594, 60740, 62222, 62558, 62666, 64072, 64074, 64144, 64148, 64192, 64296, 64444, 64864, 64888, 65135, 65195, 65454, 66666, 66814, 68102, 68108, 68306, 70105, 70210, 70518, 70555, 72148, 72296, 72324, 72444, 74222, 74666, 75925, 76114, 76222, 76228, 76684, 78666, 78962, 80012, 80018, 80044, 80066, 80088, 80090, 80120, 80132, 80135, 80180, 80185, 80216, 80240, 80296, 80370, 80396, 80432, 80540, 80720, 80792, 80888, 81212, 82666, 82738, 84108, 84252, 84324, 84518, 84666, 85185, 85555, 85765, 86222, 86666, 88108, 88132, 88148, 88198, 88296, 88444, 90135, 90555, 90666, 90810, 92138, 92276, 92444, 94282, 94666, 95555, 96108, 96592, 96864, 96888, 100022, 100030, 100090, 100110, 100135, 100148, 100222.

Some larger examples :