Číselné soustavy/Soustava o základu 72

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Příslušnost: Kusurija

Neboli dvaasedmdesátková soustava. Toto je 100 % vlastní výzkum. Ne, že by informace, zde uvedené, nebyly dosud známy (naprostá většina z nich je známa od starověku, většina malého zbytku je známa z počátků novověku a nepatrný zbytek v posledních desetiletích); vlastním výzkumem je seřazení/prezentace těch informací a naznačené souvislosti mezi nimi. Připomínky jsou vítány - ale raději v diskusi. Tam může kdokoliv i přidávat dotazy či tipy na doplnění. Uvítám i obyčejný komentář kteréhokoliv "kolemjdoucího" o tom, zda je/není článek srozumitelný. kusurija.

Pro číslice menší než 10(10) jsou (počínaje osmnáctkovou soustavou) používány náhradní symboly s přidanou nulou (0) vpředu a i pro číslice vyšší jsou používány dvojčíselné symboly. Navzájem jsou symboly odděleny dvojtečkou s výjimkou čísel jednosymbolových, tedy 00(72) - 71(72).

Číselná řada[editovat]

* (hvězdičkou) jsou označena prvočísla, ** jsou označeny mocniny prvočísel

  • Číselná řada

00, 01, 02*, 03*, 04**, 05*, 06, 07*, 08**, 09**, 10, 11*, 12, 13*, 14, 15, 16**, 17*, 18, 19*, 20, 21, 22, 23*, 24, 25**, 26, 27**, 28, 29*, 30, 31*, 32**, 33, 34, 35, 36, 37*, 38, 39, 40, 41*, 42, 43*, 44, 45, 46, 47*, 48, 49**, 50, 51, 52, 53*, 54, 55, 56, 57, 58, 59*, 60, 61*, 62, 63, 64**, 65, 66, 67*, 68, 69, 70, 71*, 01:00,

01:01*, 01:02, 01:03, 01:04, 01:05, 01:06, 01:07*, 01:08, 01:09**, 01:10, 01:11*, 01:12, 01:13, 01:14, 01:15, 01:16, 01:17*, 01:18, 01:19, 01:20, 01:21, 01:22, 01:23, 01:24, 01:25*, 01:26, 01:27, 01:28, 01:29*, 01:30, 01:31*, 01:32, 01:33, 01:34, 01:35*, 01:36, 01:37*, 01:38, 01:39, 01:40, 01:41*, 01:42, 01:43, 01:44, 01:45, 01:46, 01:47, 01:48, 01:49**, 01:50, 01:51, 01:52, 01:53**, 01:54, 01:55*, 01:56**, 01:57, 01:58, 01:59*, 01:60, 01:61, 01:62, 01:63, 01:64, 01:65*, 01:66, 01:67*, 01:68, 01:69, 01:70, 01:71, 02:00,

02:01, 02:02, 02:03, 02:04, 02:05*, 02:06, 02:07*, 02:08, 02:09, 02:10, 02:11, 02:12, 02:13*, 02:14, 02:15, 02:16, 02:17, 02:18, 02:19*, další členy řady viz tabulky...

Malá násobilka[editovat]

Malá násobilka dvaasedmdesátkové soustavy
× 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20
01 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 20
02 02 04 06 08 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40
03 03 06 09 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60
04 04 08 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 01:00 01:04 01:08
05 05 10 15 20 25 30 35 40 45 50 55 60 65 70 01:03 01:08 01:13 01:18 01:23 01:28
06 06 12 18 24 30 36 42 48 54 60 66 01:00 01:06 01:12 01:18 01:24 01:30 01:36 01:42 01:48
07 07 14 21 28 35 42 49 56 63 70 01:05 01:12 01:19 01:26 01:33 01:40 01:47 01:54 01:61 01:68
08 08 16 24 32 40 48 56 64 01:00 01:08 01:16 01:24 01:32 01:40 01:48 01:56 01:64 02:00 02:08 02:16
09 09 18 27 36 45 54 63 01:00 01:09 01:18 01:27 01:36 01:45 01:54 01:63 02:00 02:09 02:18 02:27 02:36
10 10 20 30 40 50 60 70 01:08 01:18 01:28 01:38 01:48 01:58 01:68 02:06 02:16 02:26 02:36 02:46 02:56
11 11 22 33 44 55 66 01:05 01:16 01:27 01:38 01:49 01:60 01:71 02:10 02:21 02:32 02:43 02:54 02:65 03:04
12 12 24 36 48 60 01:00 01:12 01:24 01:36 01:48 01:60 02:00 02:12 02:24 02:36 02:48 02:60 03:00 03:12 03:24
13 13 26 39 52 65 01:06 01:19 01:32 01:45 01:58 01:71 02:12 02:25 02:38 02:51 02:64 03:05 03:18 03:31 03:44
14 14 28 42 56 70 01:12 01:26 01:40 01:54 01:68 02:10 02:24 02:38 02:52 02:66 03:08 03:22 03:36 03:50 03:64
15 15 30 45 60 01:03 01:18 01:33 01:48 01:63 02:06 02:21 02:36 02:51 02:66 03:09 03:24 03:39 03:54 03:69 04:12
16 16 32 48 64 01:08 01:24 01:40 01:56 02:00 02:16 02:32 02:48 02:64 03:08 03:24 03:40 03:56 04:00 04:16 04:32
17 17 34 51 68 01:13 01:30 01:47 01:64 02:09 02:26 02:43 02:60 03:05 03:22 03:39 03:56 04:01 04:18 04:35 04:52
18 18 36 54 01:00 01:18 01:36 01:54 02:00 02:18 02:36 02:54 03:00 03:18 03:36 03:54 04:00 04:18 04:36 04:54 05:00
19 19 38 57 01:04 01:23 01:42 01:61 02:08 02:27 02:46 02:65 03:12 03:31 03:50 03:69 04:16 04:35 04:54 05:01 05:20
20 20 40 60 01:08 01:28 01:48 01:68 02:16 02:36 02:56 03:04 03:24 03:44 03:64 04:12 04:32 04:52 05:00 05:20 05:40
21 21 42 63 01:12 01:33 01:54 02:03 02:24 02:45 02:66 03:15 03:36 03:57 04:06 04:27 04:48 04:69 05:18 05:39 05:60
22 22 44 66 01:16 01:38 01:60 02:10 02:32 02:54 03:04 03:26 03:48 03:70 04:20 04:42 04:64 05:14 05:36 05:58 06:08
23 23 46 69 01:20 01:43 01:66 02:17 02:40 02:63 03:14 03:37 03:60 04:11 04:34 04:57 05:08 05:31 05:54 06:05 06:28
24 24 48 01:00 01:24 01:48 02:00 02:24 02:48 03:00 03:24 03:48 04:00 04:24 04:48 05:00 05:24 05:48 06:00 06:24 06:48
25 25 50 01:03 01:28 01:53 02:06 02:31 02:56 03:09 03:34 03:59 04:12 04:37 04:62 05:15 05:40 05:65 06:18 06:43 06:68
26 26 52 01:06 01:32 01:58 02:12 02:38 02:64 03:18 03:44 03:70 04:24 04:50 05:04 05:30 05:56 06:10 06:36 06:62 07:16
27 27 54 01:09 01:36 01:63 02:18 02:45 03:00 03:27 03:54 04:09 04:36 04:63 05:18 05:45 06:00 06:27 06:54 07:09 07:36
28 28 56 01:12 01:40 01:68 02:24 02:52 03:08 03:36 03:64 04:20 04:48 05:04 05:32 05:60 06:16 06:44 07:00 07:28 07:56
29 29 58 01:15 01:44 02:01 02:30 02:59 03:16 03:45 04:02 04:31 04:60 05:17 05:46 06:03 06:32 06:61 07:18 07:47 08:04
30 30 60 01:18 01:48 02:06 02:36 02:66 03:24 03:54 04:12 04:42 05:00 05:30 05:60 06:18 06:48 07:06 07:36 07:66 08:24
31 31 62 01:21 01:52 02:11 02:42 03:01 03:32 03:63 04:22 04:53 05:12 05:43 06:02 06:33 06:64 07:23 07:54 08:13 08:44
32 32 64 01:24 01:56 02:16 02:48 03:08 03:40 04:00 04:32 04:64 05:24 05:56 06:46 06:48 07:08 07:40 08:00 08:32 08:64
33 33 66 01:28 01:60 02:21 02:54 03:15 03:48 04:09 04:42 05:03 05:36 05:69 06:30 06:63 07:24 07:57 08:18 08:51 09:12
34 34 68 01:30 01:64 02:26 02:60 03:22 03:56 04:18 04:52 05:14 05:48 06:10 06:44 07:06 07:40 08:02 08:36 08:70 09:32
35 35 70 01:33 01:68 02:31 02:66 03:29 03:64 04:27 04:62 05:25 05:60 06:23 06:58 07:21 07:56 08:19 08:54 09:17 09:52
36 36 01:00 01:36 02:00 02:36 03:00 03:36 04:00 04:36 05:00 05:36 06:00 06:36 07:00 07:36 08:00 08:36 09:00 09:36 10:00
37 37 01:02 01:39 02:04 02:41 03:06 03:43 04:08 04:45 05:10 05:47 06:12 06:49 07:14 07:51 08:16 08:53 09:18 09:55 10:20
38 38 01:04 01:42 02:08 02:46 03:12 03:50 04:16 04:54 05:20 05:58 06:24 06:62 07:28 07:66 08:32 08:70 09:36 10:02 10:40
39 39 01:06 01:45 02:12 02:51 03:18 03:57 04:24 04:63 05:30 05:69 06:36 07:03 07:42 08:09 08:48 09:15 09:54 10:21 10:60
40 40 01:08 01:48 02:16 02:56 03:24 03:64 04:32 05:00 05:40 06:08 06:48 07:16 07:56 08:24 08:64 09:32 10:00 10:40 11:08
41 41 01:10 01:51 02:20 02:61 03:30 03:71 04:40 05:09 05:50 06:19 06:60 07:29 07:70 08:39 09:08 09:49 10:18 10:59 11:28
42 42 01:12 01:54 02:24 02:66 03:36 04:06 04:48 05:18 05:60 06:30 07:00 07:42 08:12 08:54 09:24 09:66 10:36 11:06 11:48
43 43 01:14 01:57 02:28 02:71 03:42 04:13 04:56 05:27 05:70 06:41 07:12 07:55 08:26 08:69 09:40 10:11 10:54 11:25 11:68
44 44 01:16 01:60 02:32 03:04 03:48 04:20 04:64 05:36 06:08 06:52 07:24 07:68 08:40 09:12 09:56 10:28 11:00 11:44 12:16
45 45 01:18 01:63 02:36 03:09 03:54 04:27 05:00 05:45 06:18 06:63 07:36 08:09 08:54 09:27 10:00 10:45 11:18 11:63 12:36
46 46 01:20 01:66 02:40 03:14 03:60 04:34 05:08 05:54 06:28 07:02 07:48 08:22 08:68 09:42 10:16 10:62 11:36 12:10 12:56
47 47 01:22 01:69 02:44 03:19 03:66 04:41 05:16 05:63 06:38 07:13 07:60 08:35 09:10 09:57 10:32 11:07 11:54 12:29 13:04
48 48 01:24 02:00 02:48 03:24 04:00 04:48 05:24 06:00 06:48 07:24 08:00 08:48 09:24 10:00 10:48 11:24 12:00 12:48 13:24
49 49 01:26 02:03 02:52 03:29 04:06 04:55 05:32 06:09 06:58 07:35 08:12 08:61 09:38 10:15 10:64 11:41 12:18 12:67 13:44
50 50 01:28 02:06 02:56 03:34 04:12 04:62 05:40 06:18 06:68 07:46 08:24 09:02 09:52 10:30 11:08 11:58 12:36 13:14 13:64
51 51 01:30 02:09 02:60 03:39 04:18 04:69 05:48 06:27 07:06 07:57 08:36 09:15 09:66 10:45 11:24 12:03 12:54 13:33 14:12
52 52 01:32 02:12 02:64 03:44 04:24 05:04 05:56 06:36 07:16 07:68 08:48 09:28 10:08 10:60 11:40 12:20 13:00 13:52 14:32
53 53 01:34 02:15 02:68 03:49 04:30 05:11 05:64 06:45 07:26 08:07 08:60 09:41 10:22 11:03 11:56 12:37 13:18 13:71 14:52
54 54 01:36 02:18 03:00 03:54 04:36 05:18 06:00 06:54 07:36 08:18 09:00 09:54 10:36 11:18 12:00 12:54 13:36 14:18 15:00
55 55 01:38 02:21 03:04 03:59 04:42 05:25 06:08 06:63 07:46 08:29 09:12 09:67 10:50 11:33 12:16 12:71 13:54 14:37 15:20
56 56 01:40 02:24 03:08 03:64 04:48 05:32 06:16 07:00 07:56 08:40 09:24 10:08 10:64 11:48 12:32 13:16 14:00 14:56 15:40
57 57 01:42 02:27 03:12 03:69 04:54 05:39 06:24 07:09 07:66 08:51 09:36 10:21 11:06 11:63 12:48 13:33 14:18 15:03 15:60
58 58 01:44 02:30 03:16 04:02 04:60 05:46 06:32 07:18 08:04 08:62 09:48 10:34 11:20 12:06 12:64 13:50 14:36 15:22 16:08
59 59 01:46 02:33 03:20 04:07 04:66 05:53 06:40 07:27 08:14 09:01 09:60 10:47 11:34 12:21 13:08 13:67 14:54 15:41 16:28
60 60 01:48 02:36 03:24 04:12 05:00 05:60 06:48 07:36 08:24 09:12 10:00 10:60 11:48 12:36 13:24 14:12 15:00 15:60 16:48
61 61 01:50 02:39 03:28 04:17 05:06 05:67 06:56 07:45 08:34 09:23 10:12 11:01 11:62 12:51 13:40 14:29 15:18 16:07 16:68
62 62 01:52 02:42 03:32 04:22 05:12 06:02 06:64 07:54 08:44 09:34 10:24 11:14 12:04 12:66 13:56 14:46 15:36 16:26 17:16
63 63 01:54 02:45 03:36 04:27 05:18 06:09 07:00 07:63 08:54 09:45 10:36 11:27 12:18 13:09 14:00 14:63 15:54 16:45 17:36
64 64 01:56 02:48 03:40 04:32 05:24 06:16 07:08 08:00 08:64 09:56 10:48 11:40 12:32 13:24 14:16 15:08 16:00 16:64 17:56
65 65 01:58 02:51 03:44 04:37 05:30 06:23 07:16 08:09 09:02 09:67 10:60 11:53 12:46 13:39 14:32 15:25 16:18 17:11 18:04
66 66 01:60 02:54 03:48 04:42 05:36 06:30 07:24 08:18 09:12 10:06 11:00 11:66 12:60 13:54 14:48 15:42 16:36 17:30 18:24
67 67 01:62 02:57 03:52 04:47 05:42 06:37 07:32 08:27 09:22 10:17 11:12 12:07 13:02 13:69 14:64 15:59 16:54 17:49 18:44
68 68 01:64 02:60 03:56 04:52 05:48 06:44 07:40 08:36 09:32 10:28 11:24 12:20 13:16 14:12 15:08 16:04 17:00 17:68 18:64
69 69 01:66 02:63 03:60 04:57 05:54 06:51 07:48 08:45 09:42 10:39 11:36 12:33 13:30 14:27 15:24 16:21 17:18 18:15 19:12
70 70 01:68 02:66 03:64 04:62 05:60 06:58 07:56 08:54 09:52 10:50 11:48 12:46 13:44 14:42 15:40 16:38 17:36 18:34 19:32
71 71 01:70 02:69 03:68 04:67 05:66 06:65 07:64 08:63 09:62 10:61 11:60 12:59 13:58 14:57 15:56 16:55 17:54 18:53 19:52
01:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00

Repunitová prvočísla[editovat]

Prvočísla, která se v devětašedesátkové soustavě skládají z p jedniček, kde p jsou tato: 2, 7, 13, 109, 227, ...

Převrácené hodnoty prvočísel[editovat]

l.p. - délka periody; pp=předperioda

2: 00,36:00:00:00:00:00:00:00:00:00:00:00... l.p. = 0+1pp

3: 00,24:00:00:00:00:00:00:00:00:00:00:00... l.p. = 0+1pp

4: 00,18:00:00:00:00:00:00:00:00:00:00:00... l.p. = 0+1pp

5: 00,14:28:57:43:14:28:57:43:14:28:57:43... l.p. = 4

6: 00,12:00:00:00:00:00:00:00:00:00:00:00... l.p. = 0+1pp

7: 00,10:20:41:10:20:41:10:20:41:10:20:41... l.p. = 3

8: 00,09:00:00:00:00:00:00:00:00:00:00:00... l.p. = 0+1pp

9: 00,08:00:00:00:00:00:00:00:00:00:00:00... l.p. = 0+1pp

10: 00,07:14:28:57:43:14:28:57:43:14:28:57:43... l.p. = 4+1pp

11: 00,06:39:19:45:58:65:32:52:26:13... l.p. = 10

13: 00,05:38:55:27:49:60:66:33:16:44:22:11... l.p. = 12

17: 00,04:16:67:55:04:16:67:55:04:16:67:55... l.p. = 4

19: 00,03:56:60:45:34:07:41:49:18:68:15:11... l.p. = 18

23: 00,03:09:28:12:37:40:50:06:18:56:25... l.p. = 11

29: 00,02:34:54:44:49:47:12:29:57:07:32:19... l.p. = 28

31: 00,02:23:16:18:41:58:04:46:32:37:11:44:09:20:65... l.p. = 15

37: 00,01:68:07:56:31:09:52:38:66:11:48:46... l.p. = 36

41: 00,01:54:31:43:64:70:17:40:28:07... l.p. = 10

43: 00,01:48:40:13:28:33:35:11:51:65:21:55... l.p. = 42

47: 00,01:38:21:32:12:18:27:41:26:03:04:42... l.p. = 23

53: 00,01:25:58:29:63:61:09:36:48:65:14:67... l.p. = 52

59: 00,01:15:62:17:06:07:23:13:30:36:43:67... l.p. = 58

61: 00,01:12:70:59:01:12:70:59:01:12:70:59... l.p. = 4

67: 00,01:05:26:62:23:46:15:03:16:08:42:70... l.p. = 22

71: 00,01:01:01:01:01:01:01:01:01:01:01:01... l.p. = 1

72: 00,01:00:00:00:00:00:00:00:00:00:00:00... l.p. = 0+1pp

73: 00,00:71:00:71:00:71:00:71:00:71:00:71... l.p. = 2

79: 00,00:65:44:47:28:18:16:29:11:61:04:40... l.p. = 39

83: 00,00:62:32:69:28:45:07:58:08:48:41:45... l.p. = 82

89: 00,00:58:17:57:31:39:46:08:06:33:70:27... l.p. = 44

97: 00,00:53:31:66:04:32:47:36:26:51:69:02... l.p. = 48

101: 00,00:51:23:37:56:22:58:32:57:02:09:70... l.p. = 100

103: 00,00:50:23:55:16:05:42:46:09:56:44:53... l.p. = 17

107: 00,00:48:32:21:38:25:41:03:26:17:35:47... l.p. = 106

109: 00,00:47:40:21:09:65:28:29:04:44:66:03... l.p. = 108

113: 00,00:45:63:05:52:63:51:43:69:32:35:49... l.p. = 56

...

Délky př.h. 3 - 49[editovat]

751: ... l.p. = 3

...

401: ... l.p. = 5

67961: ... l.p. = 5

5113: ... l.p. = 6 U

141276239497: ... l.p. = 7 R

1409: ... l.p. = 8

19073: ... l.p. = 8

7332299803: ... l.p. = 9

58771: ... l.p. = 10

2663: ... l.p. = 11

35311: ... l.p. = 11

1755456583: ... l.p. = 11

337: ... l.p. = 12

6133: ... l.p. = 12

19681767848550770169481: ... l.p. = 13 R

137405657593: ... l.p. = 14 U

22973401023271: ... l.p. = 15

12110113: ... l.p. = 16

59636449: ... l.p. = 16

137: ... l.p. = 17

114320887: ... l.p. = 17

327876819251626913: ... l.p. = 17

7332299803: ... l.p. = 18

3041: ... l.p. = 19

253976953: ... l.p. = 19

5799722983: ... l.p. = 19

612126391463: ... l.p. = 19

4552601: ... l.p. = 20

31720981: ... l.p. = 20

2734128569847049314367: ... l.p. = 21 U

83227: ... l.p. = 22

173779: ... l.p. = 22

3810643: ... l.p. = 22

967: ... l.p. = 23

2583712039: ... l.p. = 23

627509967075920592614984087: ... l.p. = 23

6529: ... l.p. = 24

110614812289: ... l.p. = 24

151: ... l.p. = 25

4951: ... l.p. = 25

218401: ... l.p. = 25

85847061221426088147814801: ... l.p. = 25

547: ... l.p. = 26

23011: ... l.p. = 26

46307: ... l.p. = 26

32842040219: ... l.p. = 26

48817: ... l.p. = 27

1638417241: ... l.p. = 27

33805653801602660281: ... l.p. = 27

1597: ... l.p. = 28

78653: ... l.p. = 28

1500353: ... l.p. = 28

3550541: ... l.p. = 28

929: ... l.p. = 29

5569: ... l.p. = 29

7081727420862593642417: ... l.p. = 29

280189534284009790929913: ... l.p. = 29

2011: ... l.p. = 30

87961: ... l.p. = 30

4139491: ... l.p. = 30

1303: ... l.p. = 31

9025031: ... l.p. = 31

73621529: ... l.p. = 31

26952277835027761: ... l.p. = 31

2280634106966801206561: ... l.p. = 31

193: ... l.p. = 32

13697: ... l.p. = 32

197304585248782713797057: ... l.p. = 32

6007: ... l.p. = 33

2301014272748895745273322022878287: ... l.p. = 33

307: ... l.p. = 34

1675680453531935551375874083: ... l.p. = 34

150151: ... l.p. = 35

1152761: ... l.p. = 35

109479984391: ... l.p. = 35

19602142229544019332881: ... l.p. = 35

181: ... l.p. = 36

27073: ... l.p. = 36

5157793: ... l.p. = 36

20754361: ... l.p. = 36

9103: ... l.p. = 37

3308911: ... l.p. = 37

45247303862539151x5439784363108660667233943157813521012327: ... l.p. = 37

2243: ... l.p. = 38

1188954673932515847876989341331: ... l.p. = 38

6553: ... l.p. = 39

717529351137521089659335275335101300623: ... l.p. = 39

31624001: ... l.p. = 40

16493131121929767482561: ... l.p. = 40

2543: ... l.p. = 41

70111: ... l.p. = 41

1117484436330972988340653009918665310687194149199978545468858648537: ... l.p. = 41

3749971: ... l.p. = 42

122034546775513: ... l.p. = 42

431: ... l.p. = 43

347854217969: ... l.p. = 43

6889131169459415821665219817063104319320296998224473629503604663: ... l.p. = 43

3917: ... l.p. = 44

96053: ... l.p. = 44

8428960717: ... l.p. = 44

49652099740685597: ... l.p. = 44

271: ... l.p. = 45

13591: ... l.p. = 45

40035871: ... l.p. = 45

224369849791: ... l.p. = 45

11385294504053321161: ... l.p. = 45

6717427: ... l.p. = 46

10668948094730555268888566268325219: ... l.p. = 46

106033: ... l.p. = 47

55401439: ... l.p. = 47

4725055229374532032856958586400315032250628811181173022149866870967151431: ... l.p. = 47

577: ... l.p. = 48

5281: ... l.p. = 48

327553: ... l.p. = 48

42412801: ... l.p. = 48

127021633: ... l.p. = 48

353363821008675247: ... l.p. = 49

2882323799229196166108085526249263537798935492546483369514319: ... l.p. = 49

Sledujte[editovat]