Groups in the Range until 100,000


RANGE FROM 5 UNTIL 100,000

Having 9,590 prime numbers

Size

Number of repeating groups clusters

Total number of groups in all clusters of the size

Ratio of repeating groups # to primes #,
%

  2

   257

9,492

99

  3

1,119

8,538

89

  4

1,617

5,547

58

  5

  878

2,116

22

  6

  278

   591

  6

  7

    88

    182

  2

  8

    31

     62

     0.6

  9

    13

     26

     0.3

10 

     5

     10

     0.1

11

     2

       4

       0.04

12

     1

        2

       0.02

The density of the repeating groups of the size of 2 is almost 100%
and the most diversity of them is for the size of 4

Size

Number of foursomes

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

2

  230

7,812

3

1,059

7,957

4

1,580

5,384

5

   871

 2,092

6

    277

    588

7

      88

    182

8

      31

     62

9

      13

     26

10

        5

     10

11

        2

       4

12

        1

       2

 

Some repeating irregular groups form ones of bigger size and some do not. For latter ones there are:

Size

Number of independent foursomes

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

2

111

  293

3

547

1296

4

917

2085

5

493

1053

6

146

   299

7

 41

    83

8

 13

    26

9

   5

    10

10

   2

      4

11

   0

      0

12

   1

      2

Some foursomes have all four kinds of uniform groups are full foursomes.

Size

Number 
of full foursomes

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

2

  85

6779

3

180

3988

4

  84

  916

5

  12

    65

6

   1

     4

7

   1

      4

And

Size

Number 
of full independent foursomes

Total number 
of groups
in all full independent  foursomes 
of the group size

3

3

15

4

4

22

5

2

11

These data have been gotten with the programs

eratosthenes_sieve.cpp, dynamics.cpp, allfoursomes.cpp, indfoursomes.cpp, and fullfoursomes.cpp,

executed consecutively.

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 ]