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strong primes
A prime larger than the average of the two surrounding primes. more

The first 600 strong primes :
11, 17, 29, 37, 41, 59, 67, 71, 79, 97, 101, 107, 127, 137, 149, 163, 179, 191, 197, 223, 227, 239, 251, 269, 277, 281, 307, 311, 331, 347, 367, 379, 397, 419, 431, 439, 457, 461, 479, 487, 499, 521, 541, 557, 569, 587, 599, 613, 617, 631, 641, 659, 673, 701, 719, 727, 739, 751, 757, 769, 787, 809, 821, 827, 853, 857, 877, 881, 907, 929, 937, 967, 991, 1009, 1019, 1031, 1049, 1061, 1087, 1091, 1117, 1151, 1163, 1181, 1213, 1229, 1249, 1277, 1289, 1297, 1301, 1319, 1361, 1399, 1423, 1427, 1447, 1451, 1471, 1481, 1487, 1523, 1543, 1549, 1567, 1579, 1597, 1607, 1619, 1657, 1663, 1667, 1693, 1697, 1721, 1733, 1741, 1777, 1783, 1787, 1801, 1823, 1847, 1861, 1867, 1871, 1877, 1901, 1931, 1949, 1973, 1987, 1993, 1997, 2011, 2027, 2053, 2063, 2081, 2087, 2111, 2129, 2137, 2141, 2153, 2203, 2237, 2267, 2281, 2293, 2309, 2333, 2339, 2347, 2371, 2377, 2381, 2389, 2411, 2437, 2459, 2467, 2473, 2503, 2521, 2531, 2539, 2549, 2579, 2591, 2609, 2617, 2647, 2657, 2671, 2683, 2687, 2707, 2711, 2729, 2741, 2749, 2767, 2789, 2797, 2801, 2819, 2833, 2851, 2857, 2879, 2897, 2953, 2969, 2999, 3011, 3019, 3037, 3061, 3079, 3109, 3119, 3163, 3167, 3181, 3187, 3203, 3217, 3251, 3257, 3299, 3319, 3329, 3343, 3359, 3371, 3389, 3407, 3433, 3449, 3457, 3461, 3467, 3491, 3511, 3527, 3539, 3557, 3571, 3581, 3607, 3613, 3631, 3659, 3671, 3691, 3697, 3719, 3727, 3761, 3767, 3793, 3821, 3847, 3851, 3877, 3907, 3917, 3929, 3943, 3989, 4001, 4019, 4049, 4073, 4091, 4127, 4153, 4157, 4201, 4211, 4217, 4229, 4241, 4253, 4259, 4271, 4283, 4327, 4337, 4349, 4357, 4391, 4421, 4441, 4447, 4481, 4507, 4513, 4517, 4547, 4561, 4583, 4591, 4621, 4637, 4649, 4673, 4721, 4729, 4751, 4783, 4787, 4799, 4813, 4861, 4871, 4903, 4931, 4951, 4967, 4987, 4999, 5009, 5021, 5039, 5051, 5077, 5099, 5147, 5167, 5189, 5227, 5231, 5261, 5273, 5279, 5297, 5323, 5347, 5381, 5407, 5413, 5417, 5431, 5437, 5441, 5471, 5477, 5501, 5519, 5527, 5557, 5569, 5623, 5639, 5647, 5651, 5657, 5683, 5689, 5711, 5737, 5741, 5779, 5801, 5821, 5839, 5849, 5857, 5867, 5879, 5897, 5923, 5981, 6007, 6029, 6037, 6043, 6067, 6089, 6113, 6131, 6143, 6163, 6197, 6211, 6217, 6247, 6257, 6269, 6299, 6311, 6337, 6353, 6359, 6389, 6421, 6449, 6469, 6521, 6547, 6551, 6563, 6569, 6577, 6599, 6637, 6653, 6659, 6673, 6689, 6701, 6733, 6761, 6779, 6791, 6823, 6827, 6857, 6869, 6899, 6907, 6947, 6959, 6967, 6991, 6997, 7013, 7039, 7057, 7069, 7103, 7121, 7127, 7151, 7177, 7187, 7207, 7211, 7229, 7237, 7243, 7283, 7297, 7307, 7321, 7331, 7349, 7393, 7411, 7451, 7457, 7477, 7487, 7499, 7517, 7537, 7547, 7559, 7573, 7589, 7603, 7639, 7669, 7681, 7687, 7699, 7717, 7723, 7741, 7753, 7757, 7789, 7817, 7867, 7873, 7877, 7901, 7919, 7927, 7933, 7949, 7993, 8009, 8039, 8053, 8081, 8087, 8111, 8147, 8161, 8167, 8209, 8219, 8231, 8263, 8269, 8287, 8291, 8311, 8353, 8363, 8387, 8419, 8429, 8443, 8461, 8501, 8513, 8521, 8537, 8563, 8573, 8597, 8623, 8627, 8641, 8663, 8677, 8689, 8707, 8731, 8737, 8779, 8803, 8819, 8831, 8837, 8861, 8887, 8923, 8929, 8963, 8969, 8999, 9007, 9011, 9029, 9041, 9059, 9091, 9103, 9127, 9133, 9151, 9157, 9173, 9181, 9199, 9221, 9239, 9277, 9281, 9311, 9319, 9337, 9341, 9371, 9391, 9413, 9419, 9431, 9437, 9461, 9491, 9511, 9533, 9547, 9587, 9601, 9613, 9619, 9629, 9643, 9677, 9689, 9719, 9733, 9739, 9767, 9781, 9787, 9803, 9811, 9829, 9851, 9857, 9883, 9901, 9923, 9929, 9941, 9967, 10007, 10037, 10061, 10067, 10091, 10099, 10133, 10139, 10151, 10159, 10177, 10211, 10243, 10267, 10271, 10289, 10301, 10313, 10331, 10357, 10391, 10427, 10453, 10457, 10477, 10499.

Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 2796946 values, from 11 to 99999959).

n\r 0  1 
202796946 2 
3013557711441175 3 
40139782201399124 4 
50741053780260611568664065 5 
6013557710001441175 6 
70440898498105437001487788434417498737 7 
80699723070002706980990699097 8 
9045226848071804524094804110451094480046 9 
10074105306115680007802600664065 10 
111284029306552268986295122251559313920262528287281250540276428

A pictorial representation of the table above
motab
Imagine to divide the members of this family by a number n and compute the remainders. Should they be uniformly distributed, each remainder from 0 to n-1 would be obtained in about (1/n)-th of the cases. This outcome is represented by a white square. Reddish (resp. bluish) squares represent remainders which appear more (resp. less) frequently than 1/n.