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 ]