A number whose distance to the closest prime sets a new record. more
The lonely numbers up to 10
14 :
23,
53,
120,
211,
1340,
1341,
1342,
1343,
1344,
2179,
3967,
15704,
15705,
16033,
19634,
19635,
24281,
31428,
31429,
31430,
31431,
31432,
31433,
38501,
58831,
155964,
203713,
206699,
370310,
370311,
370312,
370313,
370314,
370315,
370316,
370317,
492170,
1272749,
1357264,
1357265,
1357266,
1357267,
2010800,
2010801,
2010802,
2010803,
2010804,
2010805,
2010806,
2010807,
4652428,
4652429,
4652430,
10938023,
12623189,
20831422,
20831423,
20831424,
20831425,
20831426,
20831427,
20831428,
47326799,
47326800,
47326801,
47326802,
47326803,
122164858,
142414669,
162821917,
163710121,
325737821,
1131241763,
1791752797,
3173306951,
4302407528,
4302407529,
4302407530,
4302407531,
4302407532,
4302407533,
4302407534,
4302407535,
4302407536,
6807940367,
7174208683,
8835528511,
10726904846,
10726904847,
10726904848,
10726904849,
10726904850,
11179888193,
15318488291,
25056082298,
25056082299,
25056082300,
25056082301,
25056082302,
25056082303,
25056082304,
25056082305,
25056082306,
25056082307,
25056082308,
25056082309,
25056082310,
25056082311,
25056082312,
25056082313,
25056082314,
25056082315,
42652618572,
42652618573,
42652618574,
42652618575,
45241670743,
113482615613,
138465682247,
303371455488,
303371455489,
303371455490,
303371455491,
304599508788,
304599508789,
304599508790,
304599508791,
304599508792,
304599508793,
304599508794,
313455525683,
343834606051,
491856414677,
1346294311034,
1346294311035,
1346294311036,
1346294311037,
1346294311038,
1346294311039,
1346294311040,
1362810282439,
1480975873513,
2614941710924,
2614941710925,
5551890283531,
7177162612042,
7177162612043,
7177162612044,
7177162612045,
7177162612046,
7177162612047,
7177162612048,
7177162612049,
7177162612050,
9156364643509,
13829048560042,
13829048560043,
13829048560044,
13829048560045,
13829048560046,
13829048560047,
13829048560048,
13829048560049,
13829048560050,
13829048560051,
13829048560052,
13829048560053,
13829048560054,
13829048560055,
13829048560056,
13829048560057,
13829048560058,
13829048560059,
19581334192782,
19581334192783,
19581334192784,
19581334192785,
19581334192786,
19581334192787,
19581334192788,
19581334192789,
19581334192790,
19581334192791,
19581334192792,
19581334192793,
19581334192794,
19581334192795,
19581334192796,
19581334192797,
19581334192798,
19581334192799,
19581334192800,
19581334192801,
19581334192802,
19581334192803,
19581334192804,
19581334192805,
19581334192806,
26923643849953,
90874329411884,
90874329411885,
90874329411886,
90874329411887,
90874329411888,
90874329411889,
90874329411890,
90874329411891,
90874329411892,
90874329411893,
90874329411894,
90874329411895.
Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 211 values, from 23 to 90874329411895).
n\r | 0 | 1 |
2 | 93 | 118 | 2 |
3 | 63 | 71 | 77 | 3 |
4 | 46 | 58 | 47 | 60 | 4 |
5 | 40 | 40 | 37 | 48 | 46 | 5 |
6 | 32 | 43 | 33 | 31 | 28 | 44 | 6 |
7 | 25 | 27 | 25 | 33 | 35 | 35 | 31 | 7 |
8 | 24 | 27 | 25 | 29 | 22 | 31 | 22 | 31 | 8 |
9 | 19 | 25 | 23 | 21 | 23 | 32 | 23 | 23 | 22 | 9 |
10 | 20 | 25 | 18 | 31 | 23 | 20 | 15 | 19 | 17 | 23 | 10 |
11 | 15 | 24 | 22 | 18 | 21 | 20 | 19 | 22 | 17 | 17 | 16 |
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.