200以内质数倒数的循环节
(2009-06-11 09:19:59)
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200以内质数倒数的循环节
学者张九庆先生2008-6-14发表于博客(http://www.sciencenet.cn/u/zhangjiuqing/)上的文章,给出了分子为1、分母为100以内质数的分数转化成小数的循环节和循环节长度。本文补充101到200以内的相应结果,欢迎网友验证。(质数2,3,5不列入)
循环节长度(period m)m,衍生数集合的子集数n,m n=p-1(其中1<m≤p-1)。
200以内的质数有关数据列表如下,我们要从具体标本,。
p |
p-1分解 |
倒数的循环节 |
m |
n |
7 |
6=2×3 |
142857 |
6 |
1 |
13 |
12=22×3 |
076923 |
6 |
2 |
19 |
18=2×32 |
052631578947368421 |
18 |
1 |
41 |
40=22×5 |
02439 |
5 |
8 |
43 |
42=2×3×7 |
023255813953488372093 |
21 |
7 |
47 |
46=2×23 |
02127659574468 |
46 |
1 |
53 |
52=22×13 |
0188679245283 |
13 |
4 |
59 |
58=2×29 |
01694915254237288… |
58 |
1 |
67 |
66=2×3×11 |
014925373134328358208955 |
33 |
2 |
71 |
70=2×5×7 |
01408450704 22535211267605633802 8169 |
35 |
2 |
73 |
72=23×32 |
01369863 |
8 |
9 |
79 |
78=2×3×13 |
0126582278481 |
13 |
6 |
83 |
82=2×41 |
012048192771084337349397 |
41 |
2 |
89 |
88=23×11 |
01123595505 61797752808988764044 9438202247191 |
44 |
2 |
97 |
96=23×3 |
010309278350515463917 525773195876288659793814 690721649484536082474226 |
96 |
7 |
101 |
100=22×55 |
0099 |
4 |
25 |
103 |
102=2×3×17 |
009708737864077669902912 |
34 |
3 |
107 |
106=2×53 |
009345794392523364485981 |
53 |
2 |
109 |
108=22×33 |
0091743119266055045871559633027522935779816513761 46788990825688073394495412844036697247706422018348 623853211 |
108 |
1 |
113 |
112=24×7 |
00884955752212389380530973451327433628318584070796 4601769911504424778761061946902 203539823 |
112 |
1 |
127 |
126=2×33×7 |
007874015748031496062992 |
42 |
3 |
131 |
130=2×5×13 |
附后 |
130 |
1 |
137 |
136=23×17 |
00729927 |
8 |
17 |
139 |
138=2×3×23 |
007194244604316546762589 |
46 |
3 |
149 |
148=22×37 |
附后 |
148 |
1 |
151 |
150=2×3×52 |
006622516556291390728476 |
75 |
2 |
157 |
156=22×3×13 |
006369426751592356687898 3312101910828025477707 |
78 |
2 |
163 |
1623=2×34 |
006134969325153374233128 638036809815950920245398 |
81 |
2 |
167 |
166=2×83 |
附后 |
166 |
1 |
173 |
172=22×43 |
005780346820809248554913 |
43 |
4 |
179 |
178=2×89 |
附后 |
178 |
1 |
181 |
180=22×32×5 |
附后 |
180 |
1 |
191 |
190=2×5×19 |
005235602094240837696335 |
95 |
2 |
193 |
192=26×3 |
附后 |
192 |
|
197 |
196=22×72 |
005076142131979695431472 |
98 |
|
附:
1/131=0.007633587786259541984732
1/149=0.006711409395973154362416
1/167=0.005988023952095808383233
1/179=
0.005586592178770949720670
1/181=0
.005524861878453038674033
193370165745856353591160
110497237569060773480662
1/193=0.005181347150259067357512