A semiprime whose two prime factors have the same number of digits. more
The first 600 brilliant numbers :
4,
6,
9,
10,
14,
15,
21,
25,
35,
49,
121,
143,
169,
187,
209,
221,
247,
253,
289,
299,
319,
323,
341,
361,
377,
391,
403,
407,
437,
451,
473,
481,
493,
517,
527,
529,
533,
551,
559,
583,
589,
611,
629,
649,
667,
671,
689,
697,
703,
713,
731,
737,
767,
779,
781,
793,
799,
803,
817,
841,
851,
869,
871,
893,
899,
901,
913,
923,
943,
949,
961,
979,
989,
1003,
1007,
1027,
1037,
1067,
1073,
1079,
1081,
1121,
1139,
1147,
1157,
1159,
1189,
1207,
1219,
1241,
1247,
1261,
1271,
1273,
1333,
1343,
1349,
1357,
1363,
1369,
1387,
1403,
1411,
1457,
1501,
1513,
1517,
1537,
1541,
1577,
1591,
1633,
1643,
1649,
1679,
1681,
1691,
1711,
1739,
1763,
1769,
1817,
1829,
1843,
1849,
1891,
1909,
1927,
1943,
1961,
2021,
2047,
2059,
2077,
2117,
2173,
2183,
2201,
2209,
2231,
2257,
2263,
2279,
2291,
2407,
2419,
2449,
2479,
2491,
2501,
2537,
2573,
2581,
2623,
2627,
2701,
2747,
2759,
2773,
2809,
2813,
2867,
2881,
2911,
2923,
2993,
3007,
3053,
3071,
3127,
3139,
3149,
3233,
3239,
3293,
3337,
3397,
3403,
3431,
3481,
3551,
3569,
3589,
3599,
3649,
3713,
3721,
3763,
3827,
3869,
3901,
3953,
3977,
4087,
4171,
4183,
4187,
4189,
4307,
4331,
4399,
4453,
4489,
4559,
4661,
4717,
4757,
4819,
4891,
4897,
5041,
5063,
5141,
5183,
5251,
5293,
5329,
5429,
5561,
5609,
5723,
5767,
5893,
5917,
5963,
6059,
6241,
6319,
6497,
6499,
6557,
6887,
6889,
7031,
7081,
7387,
7663,
7921,
8051,
8633,
9409,
10201,
10403,
10609,
10807,
11009,
11021,
11227,
11413,
11449,
11639,
11663,
11881,
12091,
12317,
12769,
12827,
13081,
13231,
13493,
13589,
13837,
13843,
14017,
14039,
14111,
14279,
14317,
14351,
14659,
14803,
14873,
14933,
15049,
15151,
15251,
15347,
15481,
15553,
15707,
15857,
15943,
16129,
16157,
16171,
16241,
16459,
16463,
16637,
16789,
16799,
16837,
16867,
17063,
17113,
17161,
17201,
17399,
17441,
17473,
17653,
17741,
17767,
17819,
17869,
17947,
18079,
18203,
18209,
18281,
18419,
18437,
18511,
18643,
18769,
18857,
18871,
18923,
19043,
19153,
19177,
19291,
19321,
19367,
19493,
19511,
19519,
19549,
19673,
19729,
19781,
19879,
19897,
19939,
20099,
20227,
20291,
20413,
20437,
20453,
20497,
20567,
20651,
20687,
20701,
20711,
20819,
20989,
21037,
21079,
21209,
21293,
21311,
21353,
21473,
21509,
21583,
21691,
21733,
21809,
21823,
21877,
21971,
22201,
22261,
22331,
22487,
22499,
22523,
22577,
22657,
22663,
22733,
22801,
22879,
22927,
22969,
22987,
22999,
23129,
23213,
23381,
23393,
23449,
23533,
23587,
23701,
23707,
23711,
23843,
23861,
23999,
24047,
24139,
24257,
24287,
24289,
24307,
24341,
24503,
24511,
24523,
24613,
24617,
24649,
24743,
24797,
24823,
24881,
24883,
24931,
24961,
25019,
25021,
25159,
25199,
25217,
25273,
25283,
25351,
25397,
25573,
25591,
25651,
25777,
25787,
25807,
25853,
25877,
25957,
26051,
26069,
26123,
26167,
26219,
26269,
26329,
26441,
26471,
26549,
26563,
26569,
26671,
26797,
26827,
26857,
26969,
26989,
27007,
27029,
27089,
27161,
27169,
27221,
27233,
27263,
27331,
27359,
27371,
27383,
27499,
27641,
27661,
27707,
27889,
27913,
27977,
28013,
28103,
28141,
28199,
28321,
28363,
28381,
28417,
28459,
28531,
28583,
28667,
28757,
28783,
28829,
28841,
28891,
28907,
28943,
28997,
29041,
29083,
29143,
29149,
29177,
29213,
29321,
29329,
29353,
29503,
29539,
29591,
29593,
29639,
29651,
29719,
29737,
29747,
29893,
29929,
29987,
29999,
30049,
30067,
30179,
30193,
30227,
30281,
30301,
30353,
30397,
30523,
30551,
30607,
30623,
30629,
30847,
30929,
30967,
30997,
31007,
31099,
31133,
31243,
31301,
31309,
31313,
31351,
31373,
31411,
31439,
31459,
31553,
31571,
31613,
31621,
31753,
31831,
31861,
31877,
31897,
31921,
31937,
31979,
32017,
32033,
32041,
32111,
32231,
32239,
32387,
32399,
32437,
32639,
32651,
32743,
32761,
32849,
32881,
32899,
33017,
33043,
33109,
33127,
33221,
33227,
33233,
33277,
33389,
33401,
33431,
33463,
33491,
33499,
33667,
33673,
33823,
33899,
33919,
34037,
34081,
34093,
34117,
34121,
34163,
34189,
34277,
34387,
34393,
34417,
34427,
34453,
34547.
Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 7407840 values, from 4 to 999999863).
n\r | 0 | 1 |
2 | 4 | 7407836 | 2 |
3 | 4 | 3704879 | 3702957 | 3 |
4 | 1 | 3704760 | 3 | 3703076 | 4 |
5 | 4 | 1852489 | 1851441 | 1851443 | 1852463 | 5 |
6 | 1 | 3704877 | 1 | 3 | 2 | 3702956 | 6 |
7 | 4 | 1234959 | 1234793 | 1234285 | 1235028 | 1234316 | 1234455 | 7 |
8 | 0 | 1853197 | 1 | 1851470 | 1 | 1851563 | 2 | 1851606 | 8 |
9 | 1 | 1234840 | 1234339 | 1 | 1235002 | 1234307 | 2 | 1235037 | 1234311 | 9 |
10 | 1 | 1852488 | 0 | 1851443 | 2 | 3 | 1 | 1851441 | 0 | 1852461 | 10 |
11 | 21 | 741053 | 740590 | 740991 | 740851 | 740874 | 740546 | 740602 | 740555 | 741137 | 740620 |
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.