A member of a pair of consecutive primes whose difference is 2. more
The first 600 twin primes :
3,
5,
7,
11,
13,
17,
19,
29,
31,
41,
43,
59,
61,
71,
73,
101,
103,
107,
109,
137,
139,
149,
151,
179,
181,
191,
193,
197,
199,
227,
229,
239,
241,
269,
271,
281,
283,
311,
313,
347,
349,
419,
421,
431,
433,
461,
463,
521,
523,
569,
571,
599,
601,
617,
619,
641,
643,
659,
661,
809,
811,
821,
823,
827,
829,
857,
859,
881,
883,
1019,
1021,
1031,
1033,
1049,
1051,
1061,
1063,
1091,
1093,
1151,
1153,
1229,
1231,
1277,
1279,
1289,
1291,
1301,
1303,
1319,
1321,
1427,
1429,
1451,
1453,
1481,
1483,
1487,
1489,
1607,
1609,
1619,
1621,
1667,
1669,
1697,
1699,
1721,
1723,
1787,
1789,
1871,
1873,
1877,
1879,
1931,
1933,
1949,
1951,
1997,
1999,
2027,
2029,
2081,
2083,
2087,
2089,
2111,
2113,
2129,
2131,
2141,
2143,
2237,
2239,
2267,
2269,
2309,
2311,
2339,
2341,
2381,
2383,
2549,
2551,
2591,
2593,
2657,
2659,
2687,
2689,
2711,
2713,
2729,
2731,
2789,
2791,
2801,
2803,
2969,
2971,
2999,
3001,
3119,
3121,
3167,
3169,
3251,
3253,
3257,
3259,
3299,
3301,
3329,
3331,
3359,
3361,
3371,
3373,
3389,
3391,
3461,
3463,
3467,
3469,
3527,
3529,
3539,
3541,
3557,
3559,
3581,
3583,
3671,
3673,
3767,
3769,
3821,
3823,
3851,
3853,
3917,
3919,
3929,
3931,
4001,
4003,
4019,
4021,
4049,
4051,
4091,
4093,
4127,
4129,
4157,
4159,
4217,
4219,
4229,
4231,
4241,
4243,
4259,
4261,
4271,
4273,
4337,
4339,
4421,
4423,
4481,
4483,
4517,
4519,
4547,
4549,
4637,
4639,
4649,
4651,
4721,
4723,
4787,
4789,
4799,
4801,
4931,
4933,
4967,
4969,
5009,
5011,
5021,
5023,
5099,
5101,
5231,
5233,
5279,
5281,
5417,
5419,
5441,
5443,
5477,
5479,
5501,
5503,
5519,
5521,
5639,
5641,
5651,
5653,
5657,
5659,
5741,
5743,
5849,
5851,
5867,
5869,
5879,
5881,
6089,
6091,
6131,
6133,
6197,
6199,
6269,
6271,
6299,
6301,
6359,
6361,
6449,
6451,
6551,
6553,
6569,
6571,
6659,
6661,
6689,
6691,
6701,
6703,
6761,
6763,
6779,
6781,
6791,
6793,
6827,
6829,
6869,
6871,
6947,
6949,
6959,
6961,
7127,
7129,
7211,
7213,
7307,
7309,
7331,
7333,
7349,
7351,
7457,
7459,
7487,
7489,
7547,
7549,
7559,
7561,
7589,
7591,
7757,
7759,
7877,
7879,
7949,
7951,
8009,
8011,
8087,
8089,
8219,
8221,
8231,
8233,
8291,
8293,
8387,
8389,
8429,
8431,
8537,
8539,
8597,
8599,
8627,
8629,
8819,
8821,
8837,
8839,
8861,
8863,
8969,
8971,
8999,
9001,
9011,
9013,
9041,
9043,
9239,
9241,
9281,
9283,
9341,
9343,
9419,
9421,
9431,
9433,
9437,
9439,
9461,
9463,
9629,
9631,
9677,
9679,
9719,
9721,
9767,
9769,
9857,
9859,
9929,
9931,
10007,
10009,
10037,
10039,
10067,
10069,
10091,
10093,
10139,
10141,
10271,
10273,
10301,
10303,
10331,
10333,
10427,
10429,
10457,
10459,
10499,
10501,
10529,
10531,
10709,
10711,
10859,
10861,
10889,
10891,
10937,
10939,
11057,
11059,
11069,
11071,
11117,
11119,
11159,
11161,
11171,
11173,
11351,
11353,
11489,
11491,
11549,
11551,
11699,
11701,
11717,
11719,
11777,
11779,
11831,
11833,
11939,
11941,
11969,
11971,
12041,
12043,
12071,
12073,
12107,
12109,
12161,
12163,
12239,
12241,
12251,
12253,
12377,
12379,
12539,
12541,
12611,
12613,
12821,
12823,
12917,
12919,
13001,
13003,
13007,
13009,
13217,
13219,
13337,
13339,
13397,
13399,
13679,
13681,
13691,
13693,
13709,
13711,
13721,
13723,
13757,
13759,
13829,
13831,
13877,
13879,
13901,
13903,
13931,
13933,
13997,
13999,
14009,
14011,
14081,
14083,
14249,
14251,
14321,
14323,
14387,
14389,
14447,
14449,
14549,
14551,
14561,
14563,
14591,
14593,
14627,
14629,
14867,
14869,
15137,
15139,
15269,
15271,
15287,
15289,
15329,
15331,
15359,
15361,
15581,
15583,
15641,
15643,
15647,
15649,
15731,
15733,
15737,
15739,
15887,
15889,
15971,
15973,
16061,
16063,
16067,
16069,
16139,
16141,
16187,
16189,
16229,
16231,
16361,
16363,
16451,
16453,
16631,
16633,
16649,
16651,
16691,
16693,
16829,
16831,
16901,
16903,
16979,
16981,
17027,
17029,
17189,
17191,
17207,
17209,
17291.
Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 6849011 values, from 3 to 999999193).
n\r | 0 | 1 |
2 | 0 | 6849011 | 2 |
3 | 1 | 3424505 | 3424505 | 3 |
4 | 0 | 3424505 | 0 | 3424506 | 4 |
5 | 1 | 2282376 | 1142129 | 1141218 | 2283287 | 5 |
6 | 0 | 3424505 | 0 | 1 | 0 | 3424505 | 6 |
7 | 1 | 1370191 | 684919 | 1370316 | 1369606 | 684708 | 1369270 | 7 |
8 | 0 | 1712651 | 0 | 1712492 | 0 | 1711854 | 0 | 1712014 | 8 |
9 | 0 | 1141250 | 1140981 | 1 | 1140981 | 1142274 | 0 | 1142274 | 1141250 | 9 |
10 | 0 | 2282376 | 0 | 1141218 | 0 | 1 | 0 | 1142129 | 0 | 2283287 | 10 |
11 | 1 | 760830 | 380905 | 761122 | 761038 | 761497 | 760144 | 760786 | 760872 | 380267 | 761549 |
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.