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emirpimes  and  pandigital

First numbers that belong to both sets:

15, 177, 1202, 1346, 1366, 1454, 1766, 2402, 2426, 2642, 8345, 8735, 12605, 16265, 16535, 16615, 16795, 17645, 17735, 19595, 20795, 26165, 28705, 31945, 33815, 35285, 38035, 38245, 43705, 123771, 123807, 124779, 125781, 127047, 128127, 128211, 129111, 130827, 131151, 131343, 133359, 133593, 133689, 152571, 153507, 153597, 158757, 160773, 162147, 162879, 166899, 168999, 169581, 174621, 180399, 182739, 184389, 185883, 186051, 187203, 189951, 190011, 194241, 199041, 303843, 303861, 305247, 307011, 311739, 316599, 317019, 319857, 322053, 323061, 323151, 323823, 326631, 326913, 334281, 335163, 336759, 338061, 338763, 338817, 348303, 348321, 357387, 357537, 359427, 359673, 359787, 363567, 364569, 365847, 366393, 367833, 369177, 371949, 376653, 376863, 379497, 379623, 383151, 387183, 388023, 388581, 388893, 389199, 389289, 390381, 390633, 396471, 398661, 399207, 399981, 709557, 710187, 711219, 712227, 713571, 714603, 719337, 724629, 730839, 732441, 733017, 733143, 733353, 734829, 735753, 740127, 740769, 742143, 746943, 748623, 757257, 760107, 761199, 762843, 766851, 774957, 776361, 785283, 790791, 792507, 793389, 793461, 795273, 797241, 797343, 2217271, 2225461, 2240371, 2241911, 2243927, 2254063, 2258291, 2271143, 2271479, 2276519, 2292899, 2636221, 2637733, 2643767, 2653091, 2814371, 2821931, 2847019, 2853109, 2854187, 2895781, 3016111, 3048871, 3082429, 3110149, 3123253, 3123589, 3129749, 3139717, 3156979, 3157483, 3167647, 3167731, 3169747, 3173023, 3174227, 3214267, 3223927, 3236317, 3237437, 3237703, 3237829, 3247447, 3255623, 3255749, 3271303, 3312799, 3318203, 3318259, 3321731, 3350879, 3352517, 3363871, 3378347, 3383723, 3387797, 3400019, 3425527, 3425723, 3426199, 3487799, 3490291, 3492923, 3500483, 3502387, 3507623, 3522743, 3565079, 3570707, 3617047, 3621023, 3638579, 3645859, 3681251, 3687803, 3691751, 3694243, 3737447, 3752413, 3753533, 3755563, 3755717, 3756347, 3757607, 3758531, 3769661, 3769703, 3770557, 3771047, 3784879, 3799061, 3802589, 3803093, 3812291, 3813551, 3814727, 3823043, 3829973, 3835363, 3842363, 3844127, 3844547, 3862691, 3901597, 3902227, 3910403, 3913861, 3916843, 3922051, 3957989, 3959459, 4130987, 4300079, 4300709, 4312189, 4312553, 4314023, 4315633, 4319609, 4333469, 4341113, 4341197, 4354931, 4357451, 4376183, 4558757, 4589501, 4703797, 4704133, 4987381.

Some larger examples :