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Hogben n.  and  strong prime

First numbers that belong to both sets:

307, 757, 3907, 6007, 6163, 9901, 12433, 14281, 20593, 26083, 37057, 37831, 74257, 78121, 110557, 117307, 118681, 127807, 136531, 145543, 147073, 154057, 162007, 163621, 173473, 181903, 188791, 200257, 239611, 284623, 288907, 292141, 307471, 320923, 339307, 341641, 364213, 375157, 403861, 450913, 459007, 485113, 492103, 527803, 540961, 558757, 581407, 590593, 598303, 642403, 660157, 669943, 671581, 704761, 735307, 740461, 747361, 766501, 771763, 843643, 860257, 920641, 985057, 987043, 1005007, 1015057, 1041421, 1120423, 1145971, 1154551, 1161007, 1193557, 1204507, 1246573, 1266751, 1284823, 1319053, 1353733, 1398307, 1419673, 1462891, 1492063, 1514131, 1578793, 1596433, 1642243, 1735807, 1796941, 1848241, 1886503, 1922383, 1939057, 1964203, 2003641, 2098153, 2101051, 2171203, 2212657, 2296741, 2311921, 2360833, 2370061, 2394757, 2432041, 2460193, 2536057, 2548813, 2613073, 2626021, 2704381, 2750623, 2810653, 2840911, 2864557, 2874721, 3124057, 3134671, 3241801, 3281533, 3306943, 3358057, 3391123, 3730693, 3734557, 3812257, 3827893, 3882871, 3894703, 3910507, 3930307, 3978031, 4062241, 4090507, 4135123, 4237423, 4262161, 4307701, 4324321, 4483807, 4663441, 4676407, 4702393, 4846603, 5024323, 5127961, 5200681, 5306113, 5352283, 5403301, 5473261, 5501371, 5690611, 5700157, 5748007, 5902471, 5907331, 5965807, 6034393, 6167773, 6172741, 6227521, 6368053, 6428761, 6459223, 6530581, 6545923, 6597193, 6628051, 6705511, 6747007, 6783421, 7147603, 7195807, 7206541, 7406563, 7521307, 7781311, 7803643, 8068441, 8193907, 8205361, 8239771, 8257003, 8314573, 8326111, 8541007, 8734981, 8746807, 8800123, 8895307, 9123421, 9147601, 9165757, 9183931, 9250723, 9293353, 9305551, 9619303, 9831361, 9843907, 9881593, 9887881, 9944563, 10224007, 10268821, 10326583, 10591771, 10696171, 10768243, 10866913, 11092231, 11152261, 11529421, 11549803, 11611057, 11679307, 11816407, 11857693, 12148711, 12323611, 12358741, 12535141, 12634471, 12870157, 12985213, 13021273, 13042933, 13151503, 13289671, 13634557, 13775233, 13790083, 13842121, 13931557, 13968907, 13998823, 14156407, 14224213, 14398231, 14451403, 14718733, 14741761, 14772493, 14795563, 14864881, 15050521, 15097111, 15120433, 15206101, 15323311, 15370321, 15425257, 15638071, 15725191, 15916111, 15964021, 15972013, 16228813, 16544557, 16896211, 17143741, 17160307, 17234953, 17284807, 17635801, 17669413, 17787307, 17947933, 18126307, 18279901, 18563173, 18718603, 18944257, 19005241, 19022683, 19075057, 19136251, 19267711, 19417243, 19629331.

Some larger examples :