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emirpimes  and  wasteful n.

First numbers that belong to both sets:

26, 39, 51, 58, 62, 85, 93, 94, 143, 187, 221, 226, 302, 314, 319, 321, 326, 327, 339, 341, 381, 394, 398, 437, 493, 502, 514, 533, 538, 551, 559, 562, 586, 589, 622, 629, 667, 685, 718, 723, 734, 766, 771, 781, 794, 817, 835, 851, 871, 893, 899, 913, 921, 923, 926, 933, 951, 955, 982, 985, 998, 1177, 1243, 1313, 1417, 1469, 1507, 1651, 1703, 1717, 1727, 1807, 1903, 1937, 1969, 2018, 2041, 2042, 2062, 2066, 2098, 2206, 2234, 2258, 2402, 2413, 2426, 2446, 2458, 2461, 2462, 2474, 2602, 2603, 2614, 2642, 2654, 2669, 2818, 2831, 2839, 2878, 3013, 3043, 3046, 3047, 3062, 3063, 3091, 3093, 3097, 3098, 3099, 3103, 3106, 3117, 3131, 3134, 3142, 3151, 3153, 3166, 3173, 3189, 3197, 3207, 3247, 3261, 3291, 3309, 3317, 3326, 3327, 3334, 3338, 3401, 3418, 3419, 3421, 3442, 3446, 3453, 3459, 3473, 3503, 3513, 3518, 3543, 3554, 3579, 3603, 3622, 3629, 3639, 3646, 3651, 3653, 3667, 3669, 3679, 3687, 3693, 3694, 3707, 3737, 3743, 3754, 3777, 3778, 3809, 3814, 3817, 3826, 3831, 3839, 3866, 3891, 3893, 3898, 3903, 3921, 3946, 3949, 3957, 3958, 3959, 3963, 3979, 3981, 3986, 4117, 4121, 4138, 4162, 4166, 4174, 4178, 4181, 4198, 4309, 4313, 4321, 4322, 4369, 4387, 4511, 4531, 4537, 4538, 4541, 4553, 4562, 4573, 4574, 4577, 4579, 4594, 4714, 4727, 4742, 4754, 4771, 4954, 4981, 5006, 5053, 5062, 5078, 5086, 5095, 5111, 5114, 5123, 5143, 5155, 5165, 5177, 5182, 5191, 5311, 5314, 5317, 5318, 5339, 5342, 5345, 5354, 5359, 5363, 5366, 5371, 5374, 5378, 5386, 5398, 5414, 5422, 5426, 5435, 5438, 5447, 5455, 5458, 5465, 5482, 5498, 5513, 5515, 5539, 5543, 5545, 5554, 5567, 5582, 5585, 5587, 5594, 5603, 5606, 5611.

Some larger examples :