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emirpimes  and  frugal n.

First numbers that belong to both sets:

1849, 3481, 3721, 5041, 5329, 6889, 11449, 11881, 12769, 16129, 17161, 18769, 26569, 32041, 32761, 36481, 38809, 51529, 58081, 72361, 96721, 100489, 113569, 121801, 128881, 143641, 167281, 185761, 187489, 201601, 229441, 241081, 316969, 326041, 332929, 358801, 368449, 375769, 380689, 383161, 398161, 410881, 436921, 477481, 516961, 546121, 703921, 734449, 737881, 744769, 776161, 779689, 786769, 908209, 954529, 966289, 994009, 1018081, 1038361, 1042441, 1062961, 1067089, 1100401, 1104601, 1190281, 1194649, 1216609, 1247689, 1261129, 1324801, 1423249, 1442401, 1495729, 1510441, 1530169, 1585081, 1635841, 1646089, 1692601, 1745041, 1868689, 1885129, 2024929, 2070721, 2468041, 2679769, 3003289, 3094081, 3179089, 3193369, 3243601, 3279721, 3352561, 3463321, 3613801, 3798601, 3806401, 3972049, 3988009, 4157521, 4592449, 5013121, 5669161, 5812921, 5841889, 6086089, 6806881, 7006609, 7091569, 7219969, 7284601, 7327849, 7349521, 7360369, 7392961, 7447441, 7513081, 7579009, 7711729, 7789681, 7845601, 7856809, 8334769, 8508889, 8779369, 8994001, 9066121, 9114361, 9369721, 9406489, 9504889, 9665881, 9840769, 10118761, 10259209, 10349089, 10374841, 10426441, 10569001, 10582009, 10621081, 11042329, 11082241, 11175649, 11282881, 11363641, 11377129, 11485321, 11607649, 11950849, 11978521, 11992369, 12020089, 12327121, 12482089, 12652249, 12752041, 13010449, 13053769, 13388281, 13490929, 14145121, 14190289, 14615329, 14691889, 15124321, 15264649, 15342889, 15452761, 15547249, 15912121, 16024009, 16056049, 16168441, 16216729, 16752649, 17032129, 17048641, 17247409, 17280649, 17648401, 17732521, 18088009, 18139081, 18344089, 18826921, 18913801, 19035769, 19439281, 19545241, 19775809, 19864849, 19918369, 20079361, 20457529, 20693401, 22287841, 22306729, 22363441, 22934521, 24039409, 24433249, 24512401, 24571849, 24671089, 24870169, 24990001, 26925721, 28121809, 28185481, 30019441, 30283009, 30327049, 30946969, 31820881, 32024281, 32296489, 32364721, 32684089, 32913169, 32982049, 33884041, 33953929, 34140649, 34351321, 34421689, 34562641, 34774609, 34845409, 35438209, 36084049, 36348841, 36517849, 37075921, 37368769, 37613689, 37834801, 37982569, 38105929, 38427601, 38477209, 38576521, 38700841, 39025009, 39150049, 39300361, 39325441, 39677401, 41589601, 43151761, 43178041, 43256929, 43652449, 43811161, 45333289, 45387169, 47018449, 49182169, 50112241, 51251281, 51652969, 51739249, 54037201, 55249489, 55965361, 56235001, 56355049, 58997761, 59644729, 60202081, 60730849, 62710561, 62837329, 62932489, 64176121, 64850809, 68442529, 68740681, 70040161, 70879561.

Some larger examples :