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 |
2 | 0 | 2796946 | 2 |
3 | 0 | 1355771 | 1441175 | 3 |
4 | 0 | 1397822 | 0 | 1399124 | 4 |
5 | 0 | 741053 | 780260 | 611568 | 664065 | 5 |
6 | 0 | 1355771 | 0 | 0 | 0 | 1441175 | 6 |
7 | 0 | 440898 | 498105 | 437001 | 487788 | 434417 | 498737 | 7 |
8 | 0 | 699723 | 0 | 700027 | 0 | 698099 | 0 | 699097 | 8 |
9 | 0 | 452268 | 480718 | 0 | 452409 | 480411 | 0 | 451094 | 480046 | 9 |
10 | 0 | 741053 | 0 | 611568 | 0 | 0 | 0 | 780260 | 0 | 664065 | 10 |
11 | 1 | 284029 | 306552 | 268986 | 295122 | 251559 | 313920 | 262528 | 287281 | 250540 | 276428 |
A pictorial representation of the table above
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.