梅森和费马 素数字段


NMF(b,p,n)=(b)^(p^(n+1))-1) /(b)^(p^n)-1)
这些数字包含以下内容单一通用形式主要值得注意的数论中的数。事实上,我们得到:
-对于b=2和n=0,它们是梅森数.
-对于b=+/-2 et p=2,则为费马数.
-对于b偶数和p=2,它们是广义费马.
-对于b>2和n=0,这些是反悔以b为基数。这些数字可以被视为广义梅森,只有当p是质数。
-对于b<=-2和n=0,它们是代表基数-1.这些数字也可以被视为广义梅森,具有相同属性对于p。
-对于p=3,我们得到了形式数(b)3^n个-1) b条3^n个+1 我们可以命名广义Mersenne Fermat特别是组合形式它们的除数2千3n+1+1.

除数的一般形式这些数字中会有更多:2公里n+1+1.我们再次发现梅森数为2kp+1k2(平方公里)n+2+费马的数字为1。

对于n=1和p=m,我们还发现不一定是素数(b)+/-1) b条+1(请参见素数的新形式),但形式除数的一般更复杂。

下表总结了这些组织和特点数字:

约数

广义 M(M)埃尔森(代表。底座-1)

梅森

广义 M(M)埃尔森(反悔)

n=0

2公里+1

......

b=-6

b=-5

b=-4

b=-3

b=-2

b=2

b=3

b=4

b=5

b=6

......

......

(6第页+1) 第7页

(5第页+1)/6

(4第页+1)/5

(3第页+1)/4

(2第页+1)/3

2第页-1

(3第页-1)/2

(4第页-1)/3

(5第页-1)/4

(6第页-1)/5

......

广义 费马

费马

费马

广义 费马

p=2

k2(平方公里)n+2+1

......

b=-6

b=-5

b=-4

b=-3

b=-2

b=2

b=3

b=4

b=5

b=6

......

......

62 ^n个+1

=0模块2

42 ^n个+1

=0模块2

22 ^n个+1

22 ^n个+1

=0模块2

42 ^n个+1

=0模块2

62 ^n个+1

......

广义 梅森-弗马特

广义 梅森-弗马特

p=3

2千3n+1+1

......

b=-6

b=-5

b=-4

b=-3

b=-2

b=2

b=3

b=4

b=5

b=6

......
...... (63^n个-1)63^n个+1

=0模块3

(43^n个-1)43^n个+1 (33^n个-1)33^n个+1

=0模块3

(23^n个+1)23^n个+1 (33^n个+1)33^n个+1

=0模块3

(53^n个+1)53^n个+1 (63^n个+1)63^n个+1 ......

第页

2公里n+1+1

......
 
 
 
 
 
 
 
 
 
 
......

......

 
 
 
 
 
 
 
 
 
 
......


 

梅森油田

p的素数或prps

第页<

.......

...

... 

(104^p-1)/103
97,263,5437
5438

.......

...

... 

(99^p-1)/98
3,5,37,47,383,5563
5564

.......

...

... 

(95^p-1)/94
7,523,9283,10487,11483
11484

。。。。。。。

...

... 

(90^p-1)/89
3,19,975209年
5210
(89^p-1)/88
3,7,43,47,71,109,571,11071
11972

.......

...

... 

(82^p-1)/81

2,23,31,41,7607

7608

.......

...

... 

(70^p-1)/69
2,29,59,541,761,1013,11621
11622
(69^p-1)/68
3,61,2371,3557,8293
8294

.......

...

... 

(67^p-1)/66
19,367,1487,3347,4451,10391
10392

.......

...

... 

(62^p-1)/61
3,5,17,47,163,173,757,4567,9221,10889
10890

.......

...

... 

(59^p-1)/58

3,13,479,12251

12252

.......

...

... 

(50^p-1)/49

3,5,127,139,347,661,2203,6521

20000

(49^p-1)/48

 

-

(48^p-1)/47

19,269,349,383,1303,15031

20000

(47^p-1)/46

12718013年

20000

(46^p-1)/45

2,7,19,67,211,433,2437,2719,19531

20000

(45^p-1)/44

19,53,167,3319,11257

20000

(44^p-1)/43

5,31,167

20000

(43^p-1)/42

5,13,6277

20000

(42^p-1)/41

2,1319

20000

(41^p-1)/40

3,83,269,409,1759,11731

20000

(40^p-1)/39

2,5,7,19,23,29,541,751,1277

20000

(39^p-1)/38

349,631,4493,16633

20000

(38^p-1)/37

3,7,401,449

20000

(37^p-1)/36

13,71,181,251,463,521,7321

20000

(36^p-1)/35

2

-

(35^p-1)/34

313,1297

20000

(34^p-1)/33

13,1493,5851,6379

20000

(33^p-1)/32

3,197,3581,6871

20000

(32^p-1)/31

 

20000

(31^p-1)/30

7,17,31,5581,9973

20000

(30^p-1)/29

2,5,11,163,569,1789,8447

20000

(29^p-1)/28

5,151,3719

20000

(28^p-1)/27

2,5,17,457,1423

20000

(27^p-1)/26

-

(26^p-1)/25

7,43347124211247326717

30000

(25^p-1)/24

 

-

(24^p-1)/23

3,5,19,53,71,653,661,10343

30000

(23^p-1)/22

5,3181

30000

(22^p-1)/21

2,5,79,101,359,857,4463,9029,27823

30000

(21^p-1)/20

3,11,17,43,271

30000

(20^p-1)/19

3,11,17,1487

30000

(19第页-1)/18

19,31,47,59,61,107,337,1061,9511,22051

30000

(18第页-1)/17

2,25667,28807

30000

(17第页-1)/16

3,5,7,11,47,71,419,4799

30000

(16第页-1)/15

2

-

(15)第页-1)/14

3,43,73,487,2579,8741

30000

(14第页-1)/13

3,7,19,31,41,2687,19697,..,59693,67421

30000

(13第页-1)/12

5,7,137,283,883,991,1021,1193,3671,18743,31751

31752

(12第页-1)/11

2,3,5,19,97,109,317,353,701,9739,14951,37573,46889

46890

(11第页-1)/10

17,19,73,139,907,1907,2029,4801,5153,10867,20161

41000

(10第页-1)/9 

2,19,2331710314908186453109297270343

300000

(9第页-1)/8

 

-

(8第页-1)/7

-
(7第页-1) 第6页

5,1313114916991422135201126037

126038
 (6第页-1)/5

2,3,7,29,71,127,271,509,1049,6389,6883,10613,19889,...,79987

50000
 (5第页-1)/4

3,7,11,13,47,127,149,181,619,929,3407,10949,13241,13873,16519

60000

 (4第页-1)/3

2

-

 (3第页-1)/2

3,7,13,71,103,541,1091,1367,1627,4177,9011,9551,36913,43063,49681,
57917

90000

2第页-1

2,3,5,7,13,17,19,31,61,89,107,127,521,607,1279,2203,2281,3217,4253,
4423,9689,9941,11213,19937,21701,23209,44497,86243,110503,132049,
216091,756839,859433,1257787,1398269,2976221,3021377,6972593,
13466917,..,20996011,..,24036583,..,25964951,..,30402457,..,32582657,
..,37156667,..,43112609

18816700

 (2第页+1)/3

3,5,7,11,13,17,19,23,31,43,61,79,101,127,167,191,199,313,347,701,1709,
2617,3539,5807,10501,10691,11279,12391,14479,42737,83339,95369,
117239,127031,138937,141079,267017,269987,374321,..,986191

720000

(3第页+1) 第4页

3,5,7,13,23,43,281,359,487,577,1579,1663,1741,3191,9209,11257,12743,
13093,17027,26633,...,104243,。。。,134227

85000

(4第页+1)/5

-

(5第页+1)/6

5,67,101,103,229,347,4013,23297,30133

65000

(6第页+1)/7

3,11,31,43,47,59,107,811,2819,4817,9601,33581,38447,41341

55000
(7第页+1)/8

3,17,23,29,47,61,1619,18251

55000

(8第页+1)/9

 

-

(9第页+1)/10

3,59,223,547,773,1009,1823,3803,49223

49224

(10第页+1)/11

5,7,19,31,53,67,293,641,2137,3011

43000

(11第页+1)/12
5,7,179,229,439,557,6113
40000
(12第页+1)/13
5,11,109,193,1483,11353,21419,21911,24071
40000
(13第页+1)/14
3,11,17,19,919,1151,2791,9323
40000
(14第页+1)/15
7,53,503,1229,22637
30000
(15)第页+1)/16
3,7,29,1091,2423
30000
(16第页+1)/17
3,5,7,23,37,89,149,173,251,307,317,30197

40000

(17第页+1)/18
7,17,23,47,967,6653,8297
30000
(18第页+1)/19
3,7,23,73,733,941,1097,1933,4651
30000
(19第页+1)/20
17,37157163631735126183
30000

(20^p+1)/21

2,5,79,89,709,797,1163,6971

30000

(21^p+1)/22

3,5,7,13,3734717597

30000

(22^p+1)/23

3,5,13,43,79,101,107,227,353,7393

30000

(23^p+1)/24

11,13,67,109,331,587

20000

(24^p+1)/25

2,7,11,19,2207,2477,4951

20000

(25^p+1)/26

3,7,23,29,59,1249,1709,1823,1931,3433,8863

20000

(26^p+1)/27

11,109,227,277,347,857,2297,9043

20000

(27^p+1)/28

 

-

(28^p+1)/29

3,19,373,419,491,1031

20000

(29^p+1)/30

7
20000

(30便士+1)/31

2,139,173,547,829,2087,2719,3109,10159
20000

(31便士+1)/32

109,461,1061

20000

(32^p+1)/33

2

20000

(33^p+1)/34

5,67,157,12211

20000

(34^p+1)/35

20000

(35^p+1)/36

11,13,79,127,503,617,709,857,1499,3823

20000

(36便士+1)/37

31,191,257,367,3061

20000

(37^p+1)/38

5,7,2707

20000

(38^p+1)/39

2,5,167,1063,1597,2749,3373,13691

20000

(39^p+1)/40

3,13,149,15377

20000

(40便士+1)/41

53,6712175867614311681

20000

(41便士+1)/42

17,691

20000

(42^p+1)/43

2,3709163717911

20000

(43便士+1)/44

5,7,19,251,277,383,503,3019,4517,9967

20000

(44^p+1)/45

2.7个

20000

(45^p+1)/46

103,157

20000

(46^p+1)/47

7,23,59,71,107,223,331,2207,6841

20000

(47^p+1)/48

5,19,23,79,1783,7681

20000

(48^p+1)/49

2,5,17,131

20000

(49^p+1)/50

7,19,37,83,1481,12527

20000

(50^p+1)/51

1153

20000

......

...

...

(58便士+1)/59

3,17,1447,11003

11004

......

...

...

(94^p+1)/95
71,307,613,1787,3793,10391
10392

......

...

...

(100^p+1)/101
3,293,461,11867
11868

......

...

...

(256第页+1)/257
5,13
7000
......
...
...
(1296^p+1)/1297
3,2153,3517
3518
......
...
...
(65536第页+1)/65537
239
7000
......

...

...


  


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创建者亨利·利夫奇茨:1999年4月12日,上次修改:2008年9月21日。