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strong prime  and  Ulam n.

First numbers that belong to both sets:

11, 97, 197, 431, 673, 739, 751, 991, 1721, 2371, 2789, 2833, 2897, 3109, 3217, 3371, 3527, 3671, 3691, 4153, 4211, 4517, 4729, 4903, 6029, 6569, 7297, 7537, 7559, 7603, 8167, 8573, 8969, 9311, 9511, 9619, 9643, 9851, 9941, 10271, 10391, 10457, 10831, 11197, 11273, 11969, 12143, 12917, 13159, 13411, 13721, 13799, 13873, 13931, 14281, 14557, 14923, 15053, 15121, 15661, 16741, 16829, 17623, 17909, 18251, 18427, 19031, 19121, 19427, 19681, 20323, 20389, 20441, 20543, 20807, 20849, 20939, 21017, 21191, 22381, 22469, 22637, 23053, 23549, 23827, 23869, 23957, 24091, 25169, 25237, 25469, 25601, 26317, 26813, 26879, 26891, 27329, 27673, 27817, 27883, 27893, 28081, 28643, 29017, 29147, 29437, 29789, 29833, 30197, 30241, 30703, 30803, 31189, 31387, 31663, 31883, 32057, 32189, 32233, 32257, 32411, 32423, 32687, 32707, 33049, 33479, 33613, 33809, 34583, 34757, 34847, 34913, 35729, 36599, 36809, 37217, 37501, 37547, 37811, 38197, 38669, 39157, 39209, 39409, 39509, 39749, 40237, 42407, 42451, 42859, 43573, 43961, 44159, 44699, 44909, 45361, 46099, 46229, 46549, 47111, 47279, 47741, 48017, 48479, 48821, 49031, 50111, 50527, 50549, 50891, 51257, 51607, 51971, 52103, 52147, 52433, 52667, 52709, 53161, 53549, 53681, 53813, 54133, 54287, 54409, 54629, 55103, 55541, 55817, 56359, 56731, 56767, 56921, 56941, 57131, 57163, 57527, 57649, 59863, 59951, 60029, 60161, 60811, 61043, 61483, 62297, 62861, 63059, 63487, 64811, 65371, 65407, 65647, 65713, 65867, 66617, 66749, 67181, 67391, 68501, 68567, 68633, 69109, 69857, 69991, 70223, 70529, 70663, 71479, 71711, 72493, 72889, 72901, 73471, 73517, 74099, 74287, 74377, 74521, 74827, 75323, 75479, 75931, 76603, 76943, 77549, 77681, 78157, 78509, 79039, 79103, 79841, 79997, 80207, 80447, 80527, 80701, 81097, 81551, 82003, 82067, 82301, 82609, 82651, 83833, 84317, 85199, 85331, 85817, 87103, 87403, 87613, 87679, 87853, 88117, 89101, 89561, 90401, 90731, 90971.

Some larger examples :