Groups in the Range until 1,000,000

There are in the range of primes until 1,000,000:

78,498 prime numbers

Repeating groups

Size

Number of
repeating groups
clusters

Total number of groups in all clusters of the size

Ratio of repeating groups # to primes #, %



2



     674



78,298

 

99.75

Comparing
 
with range
until

100,000





increase

3

  4,942

75,170

95.76

4

12,283

58,724

74.81

5

10,220

27,661

35.24

6

  3,269

  7,073

  9.01

7

     653

  1,331

  1.70

decrease

8

     141

     283

  0.36

9

       34

       68

  0.09

 10

         7

       14

  0.02

 11

       2

         4

  0.005
 12

       1

         2   0.003
              The same in the range until 100,000

The density of the repeating groups of the size of 2
aspires to 100%
 

Repeating irregular groups
 

Size

Number
of foursomes

Total number
of irregular groups 
in all foursomes
of the group size

2

     629

66,919

3

  4,776

71,012

4

12,155

57,759

5

10,162

27,462

6

 3,254

  7,037

7

    652

  1,329

8

    140

     281

9

      34

       68

10

        7        14

11

       2          4

12

       1

         2

                         The same in the range until 100,000


666666666666

Regular Groups

Type Size 2 3 4 5 6 7 8 9 10
Symmetriads 6728 54 709 1 96   14   5
Curls   3282 246 316 27 24 5  2 1
Stairs   4427 466 46 5 1        
Flats   2993 229              
Zigzags     425 51 5          

 

 

Up ] Introduction of Variation ] Regular and Repeating Groups ] Groups in the Range until 100,000 ] [ Groups in the Range until 1,000,000 ] Key of Primes Structure ] Distribution of gaps and variations ] Boolean Algebra of Classes ] Consecutive primes ] Groups of primes in the infinite set ] Groups of primes in a limited range ] We have for each kind of regular and repeating groups ]

 
Last updated 03/27/2009
Copyright 2003 Michael Chassis. All rights reserved.