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alternating n.  and  unprimeable n.

First numbers that belong to both sets:

325, 890, 892, 894, 896, 898, 1070, 1072, 1074, 1076, 1078, 1410, 1412, 1414, 1416, 1418, 1670, 1672, 1674, 1676, 1678, 1850, 1852, 1854, 1856, 1858, 1890, 1892, 1894, 1896, 1898, 2105, 2185, 2325, 2365, 2565, 2585, 2945, 2985, 3050, 3052, 3054, 3056, 3058, 3090, 3092, 3094, 3096, 3098, 3230, 3232, 3234, 3236, 3238, 3470, 3472, 3474, 3476, 3478, 3810, 3812, 3814, 3816, 3818, 3890, 3892, 3894, 3896, 3898, 4105, 4145, 4165, 4185, 4305, 4385, 4745, 4765, 4925, 5210, 5212, 5214, 5216, 5218, 5250, 5252, 5254, 5256, 5258, 5450, 5452, 5454, 5456, 5458, 5490, 5492, 5494, 5496, 5498, 5610, 5612, 5614, 5616, 5618, 5670, 5672, 5674, 5676, 5678, 6185, 6505, 6725, 6745, 6925, 7090, 7092, 7094, 7096, 7098, 7270, 7272, 7274, 7276, 7278, 7610, 7612, 7614, 7616, 7618, 7650, 7652, 7654, 7656, 7658, 7830, 7832, 7834, 7836, 7838, 7890, 7892, 7894, 7896, 7898, 8185, 8305, 8345, 8725, 8905, 8985, 9030, 9032, 9034, 9036, 9038, 9070, 9072, 9074, 9076, 9078, 9210, 9212, 9214, 9216, 9218, 9450, 9452, 9454, 9456, 9458, 9650, 9652, 9654, 9656, 9658, 9890, 9892, 9894, 9896, 9898, 10125, 10385, 10545, 10745, 10765, 10925, 10965, 12125, 12185, 12365, 12385, 14125, 14165, 14185, 14525, 14585, 14705, 14905, 16165, 16325, 16505, 16585, 18105, 18385, 18565, 18725, 18765, 18905, 18925, 18965, 18985, 21070, 21072, 21074, 21076, 21078, 21090, 21092, 21094, 21096, 21098, 21230, 21232, 21234, 21236, 21238, 21250, 21252, 21254, 21256, 21258, 21290, 21292, 21294, 21296, 21298, 21450, 21452, 21454, 21456, 21458, 21470, 21472, 21474, 21476, 21478, 21630, 21632, 21634, 21636, 21638, 21650, 21652, 21654, 21656, 21658, 21690, 21692, 21694, 21696, 21698, 23210, 23212, 23214, 23216, 23218, 23230, 23232, 23234, 23236, 23238, 23610, 23612, 23614, 23616, 23618, 23650, 23652, 23654, 23656, 23658.

Some larger examples :