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Chen prime  and  Hogben n.

First numbers that belong to both sets:

3, 7, 13, 31, 157, 211, 307, 2971, 3307, 3541, 3907, 5701, 6007, 6481, 8011, 8191, 9901, 13807, 21757, 26407, 35911, 37831, 78121, 98911, 108571, 117307, 163621, 171811, 262657, 276151, 281431, 292141, 327757, 375157, 415381, 558757, 570781, 628057, 792991, 800131, 809101, 860257, 1041421, 1139557, 1145971, 1154551, 1278031, 1305307, 1573771, 1735807, 1796941, 2075041, 2115571, 2233531, 2296741, 2311921, 2339371, 2370061, 2626021, 2864557, 2891701, 4062241, 4262161, 4307701, 4433131, 4590307, 4859821, 5087281, 5127961, 5333791, 5473261, 5690611, 5714491, 5772007, 5907331, 7195807, 7455631, 7482961, 8378131, 9147601, 9305551, 9606901, 9831361, 9843907, 10243201, 10320157, 10461991, 10591771, 10873507, 12106921, 12127807, 12549307, 12634471, 12920431, 13355371, 14330011, 14741761, 15370321, 16140307, 16871557, 17143741, 18126307, 19005241, 19320421, 19691407, 19958557, 20607061, 23790007, 25953931, 26188807, 26322031, 26651407, 27725491, 28010557, 28681381, 28810057, 29057491, 29219431, 29806141, 30079741, 31837807, 33171841, 33553057, 34745131, 36572257, 36790291, 38075071, 38682181, 39507511, 40379671, 41222821, 41402791, 41570257, 42113611, 42738907, 42935257, 43593007, 43751611, 44482231, 46342057, 47272501, 47824141, 47851807, 48226081, 49667257, 50630341, 54250591, 54649057, 55138051, 56392591, 56467711, 56934571, 56964757, 59992771, 60101257, 60132271, 60614011, 61787461, 62244211, 62924557, 64008001, 64440757, 64794451, 64971661, 66137557, 67166221, 68021257, 68550121, 69297301, 70568401, 71732431, 72428611, 72547807, 73265041, 74399251, 76221631, 77484007, 77572057, 80021971, 80183071, 81640261, 82310257, 86871721, 90335521, 93325261, 93886411, 95072251, 96049801, 97663807, 98000101, 99012451, 99151807, 99510601, 99790111.