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prime n.  and  self n.

First numbers that belong to both sets:

3, 5, 7, 31, 53, 97, 211, 233, 277, 367, 389, 457, 479, 547, 569, 613, 659, 727, 839, 883, 929, 1021, 1087, 1109, 1223, 1289, 1447, 1559, 1627, 1693, 1783, 1873, 2099, 2213, 2347, 2437, 2459, 2503, 2549, 2593, 2617, 2683, 2729, 2819, 2953, 3023, 3067, 3089, 3313, 3359, 3449, 3517, 3539, 3583, 3673, 3719, 3853, 3919, 3943, 4057, 4079, 4259, 4327, 4349, 4483, 4663, 4909, 4933, 4999, 5113, 5227, 5519, 5563, 5653, 5743, 5923, 6011, 6037, 6217, 6329, 6373, 6553, 6619, 6709, 6733, 6823, 6911, 7001, 7027, 7229, 7699, 7723, 7789, 7879, 7901, 8039, 8219, 8263, 8353, 8419, 8443, 8599, 8623, 8689, 8779, 9029, 9319, 9343, 9433, 9521, 9679, 9769, 9791, 9859, 9949, 10111, 10133, 10177, 10223, 10267, 10289, 10313, 10357, 10513, 10559, 10627, 10739, 11213, 11257, 11279, 11369, 11437, 11503, 11527, 11549, 11593, 11617, 11863, 11953, 12113, 12157, 12269, 12517, 12539, 12583, 12763, 12853, 12919, 13009, 13147, 13259, 13327, 13417, 13619, 13933, 13999, 14159, 14249, 14293, 14519, 14563, 14653, 14923, 15149, 15193, 15217, 15329, 15373, 15619, 15643, 15733, 15823, 15889, 16001, 16139, 16183, 16229, 16273, 16319, 16363, 16453, 16519, 16633, 16699, 16811, 16879, 16901, 17419, 17443, 17509, 17599, 17623, 17891, 17959, 17981, 18119, 18253, 18433, 18521, 18523, 18679, 18701, 18859, 19219, 19309, 19333, 19421, 19423, 19489, 19759, 19961, 20123, 20347, 20369, 20549, 20593, 20639, 20773, 21023, 21067, 21089, 21157, 21179, 21247, 21269, 21313, 21493, 21517, 21673, 21943, 22079, 22147, 22259, 22303, 22349, 22483, 22573, 22619, 23159, 23203, 23227, 23293, 23339, 23473, 23563, 23719, 23743, 23833, 23899, 24103, 24239, 24329, 24373, 24419, 24709, 24733, 24799, 24821, 24889, 24979, 25117, 25183, 25229, 25453, 25609, 25633, 25969, 26083, 26263, 26711, 26801, 26891, 26959, 26981, 27073, 27253, 27409, 27611, 27701, 27791.

Some larger examples :