A composite number that begins with the concatenation of its distinct prime factors. more
The enlightened numbers up to 5.57×10
11 :
250,
256,
2048,
2176,
2304,
2500,
2560,
2744,
23328,
25000,
25600,
119911,
219488,
236196,
250000,
256000,
262144,
290912,
2097152,
2238728,
2317312,
2359296,
2370816,
2500000,
2560000,
3515625,
3720087,
5117695,
13436683,
21359416,
23592960,
23887872,
25000000,
25600000,
27294568,
29090912,
235929600,
237180384,
248543744,
250000000,
256000000,
268435456,
271351808,
275365888,
353109375,
358722675,
387420489,
595238125,
761743661,
2147483648,
2317206624,
2324522934,
2347906338,
2359296000,
2377970784,
2378170368,
2500000000,
2560000000,
2717384704,
3486784401,
3573588375,
21109276672,
21923380546,
22707961856,
23219011584,
23573790720,
23592960000,
23679672516,
23702740992,
23727920916,
24312841216,
25000000000,
25600000000,
25711938560,
25735718750,
27682574402,
28397229568,
31381059609,
35214691275,
35595703125,
37822859361,
57382399375,
57736239625,
137858491849,
231928233984,
232335362178,
235092492288,
235737907200,
235929600000,
237916127232,
250000000000,
256000000000,
257119385600,
257357187500,
261993005056,
273162960896,
274877906944,
323754489243,
331353897741,
351189498825,
351353851875,
353797811253,
361881028863,
373714754427,
511374199655,
557041015625.
Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 106 values, from 250 to 557041015625).
n\r | 0 | 1 |
2 | 78 | 28 | 2 |
3 | 45 | 41 | 20 | 3 |
4 | 71 | 14 | 7 | 14 | 4 |
5 | 44 | 19 | 11 | 17 | 15 | 5 |
6 | 27 | 7 | 17 | 18 | 34 | 3 | 6 |
7 | 23 | 21 | 10 | 14 | 15 | 9 | 14 | 7 |
8 | 66 | 9 | 5 | 6 | 5 | 5 | 2 | 8 | 8 |
9 | 43 | 4 | 5 | 1 | 15 | 11 | 1 | 22 | 4 | 9 |
10 | 30 | 5 | 9 | 4 | 12 | 14 | 14 | 2 | 13 | 3 | 10 |
11 | 7 | 8 | 8 | 18 | 9 | 12 | 7 | 8 | 20 | 7 | 2 |
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.