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emirpimes  and  inconsummate n.

First numbers that belong to both sets:

62, 326, 381, 493, 497, 533, 553, 623, 723, 771, 926, 933, 1041, 1043, 1046, 1371, 1382, 1437, 1497, 1527, 1538, 1641, 1983, 2042, 2426, 2603, 2642, 3046, 3053, 3093, 3153, 3207, 3247, 3291, 3317, 3327, 3437, 3554, 3647, 3651, 3665, 3687, 3707, 3713, 3743, 3809, 3831, 3866, 3869, 3983, 3986, 4109, 4121, 4151, 4183, 4187, 4198, 4309, 4313, 4319, 4538, 4541, 4553, 4571, 4594, 4742, 5177, 5342, 5363, 5378, 5426, 5615, 5645, 5942, 6038, 6437, 6887, 7082, 7181, 7223, 7311, 7377, 7421, 7431, 7445, 7538, 7571, 7593, 7601, 7646, 7706, 7709, 7715, 7737, 8153, 8159, 8306, 8309, 8345, 8522, 8546, 8549, 8561, 8705, 8777, 8945, 9026, 9038, 9147, 9263, 9267, 9326, 9363, 9593, 9627, 9641, 9671, 9753, 9777, 9917, 9921, 9959, 9977, 9987, 9995, 10217, 10237, 10327, 10347, 10367, 10517, 10577, 10637, 10677, 10699, 10874, 10893, 11031, 11195, 11477, 11531, 11582, 11603, 11723, 11945, 11993, 12053, 12086, 12587, 12599, 12602, 12605, 13307, 13382, 13637, 13647, 13657, 13703, 13742, 13814, 13922, 13991, 14054, 14237, 14255, 14277, 14291, 14318, 14367, 14414, 14417, 14429, 14439, 14483, 14486, 14493, 14681, 14687, 14702, 14727, 14757, 14765, 14799, 14811, 14855, 14857, 14873, 14909, 14979, 15153, 15177, 15209, 15297, 15305, 15338, 15419, 15482, 15537, 15815, 15863, 15893, 15927, 15989, 16251, 16257, 16409, 16517, 16997, 17049, 17147, 17426, 17607, 17687, 17717, 18098, 18317, 18437, 18641, 18653, 18737, 18782, 18807, 19083, 19217, 19226, 19262, 19265, 19445, 19547, 19607, 19643, 19653, 19715, 19742, 19743, 19814, 19823, 20093, 20153, 20291, 20321, 20354, 20365, 20489, 20621, 20687, 20699, 20837, 20885, 20957, 20987, 22982, 24482, 24731, 24737, 26045, 26126, 26507, 26753, 26837, 28103, 28121, 28214, 28331, 28361, 28442, 28481, 28487, 28511, 28694, 28781, 28799, 28829, 28838, 28862, 28922, 30257, 30281, 30311, 30329.

Some larger examples :