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emirpimes  and  super-d n.

First numbers that belong to both sets:

169, 319, 335, 339, 381, 511, 581, 781, 1046, 1057, 1059, 1067, 1119, 1145, 1169, 1219, 1454, 1469, 1569, 1731, 1761, 1769, 1923, 1969, 1981, 2219, 2231, 2462, 2474, 2479, 2627, 2669, 2818, 2831, 2881, 3131, 3317, 3326, 3327, 3334, 3338, 3365, 3385, 3419, 3431, 3481, 3669, 3831, 3869, 3981, 4181, 4319, 4369, 4531, 4594, 4781, 4981, 5111, 5131, 5318, 5342, 5414, 5579, 5645, 6031, 6431, 6631, 7081, 7131, 7169, 7181, 7269, 7274, 7373, 7419, 7423, 7431, 7531, 7619, 7646, 7737, 7814, 7831, 7834, 7837, 7981, 8131, 8902, 9034, 9069, 9326, 9481, 9569, 9617, 9727, 9731, 9895, 10033, 10057, 10081, 10119, 10219, 10231, 10319, 10358, 10363, 10454, 10489, 10495, 10517, 10519, 10523, 10537, 10541, 10546, 10551, 10553, 10558, 10561, 10577, 10594, 10603, 10618, 10623, 10637, 10643, 10661, 10671, 10673, 10677, 10694, 10699, 10702, 10705, 10713, 10717, 10721, 10919, 10981, 11006, 11031, 11181, 11219, 11231, 11531, 11569, 11581, 11667, 11669, 11761, 11769, 11881, 11963, 12031, 12067, 12081, 12169, 12182, 12419, 12469, 12471, 12494, 12531, 12631, 12701, 12706, 12707, 12769, 12797, 13011, 13058, 13269, 13459, 13819, 13834, 14005, 14019, 14069, 14131, 14219, 14261, 14269, 14285, 14374, 14471, 14509, 14531, 14569, 14631, 14681, 14701, 14702, 14719, 14873, 14881, 14962, 15019, 15127, 15153, 15389, 15419, 15441, 15681, 15769, 15781, 15815, 15931, 16019, 16123, 16145, 16213, 16255, 16313, 16331, 16442, 16466, 16517, 16531, 16591, 16781, 16837, 16859, 16969, 17063, 17219, 17237, 17354, 17369, 17373, 17531, 17638, 17639, 17645, 17647, 17726, 17769, 17781, 17869, 18035, 18219, 18393, 18619, 18623, 18643, 18769, 18877, 18969, 19011, 19169, 19265, 19297, 19331, 19369, 19419, 19555, 19637, 19731, 19769, 19814, 19831, 19903, 19931, 19933, 19969, 20081, 20131, 20137, 20153, 20203, 20285, 20362, 20381, 22081, 22309, 22313, 22327, 22331, 22373, 22579, 22663.

Some larger examples :