dedanoe
As sum A ss um
рем: (се надевам немате против шо е на инглиш)
highly divergent way of knowing the set of all them primes
let N be the greatest known prime and F(N) be the primal factorial of N (for instance if N is 5 than F(N) is 2 x 3 x 5 or if N is 11 then F(N) is 2 x 3 x 5 x 7 x 11) then for some prime g between 2 and N including 2 and N the g-th brotherhood of primes is B(g) = {F(N)/g x {k | (0<k<g)} (+/-) {all the elements of type g^n where n is natural and g^n is less than F(N)/g except if g=2 then n is natural and g^(n-1) is less than F(N)/g)}}.
THESIS: The union of all the brotherhoods B(g) for g prime between 2 and N including 2 and N is the set of ALL THE PRIMES AND PRIMES ALONE from 1 to F(N).
EXAMPLE: N = 5; F(N) = 2 x 3 x 5 = 30;
B(2) = {15 x {1} (+/-) {2^1, 2^2, 2^3, 2^4}} = {13, 17, 11, 19, 7, 23, 29, 1}
B(3) = {10 x {1, 2} (+/-) {3^1, 3^2}} = {7, 13, 1, 19, 17, 23, 11, 29}
B(5) = {6 x {1, 2, 3, 4} (+/-) {5^1}} = {1, 11, 7, 17, 13, 23, 19, 29}
it occurs that B(2) = B(3) = B(5) but that doesn't have to be the case for larger N; all the primes up to F(5)=30 are {2, 3, 5} U B(2) U B(3) U B(5) = {1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29}. Now the method may continue for N = 29 and F(N) = 6'469'693'230 it is some number between 30^6 and 30^7; 30 being F(5); which only speaks in favor of how fast this divergence in obtaining the unknown primes is. you'll check it out right...!?!
highly divergent way of knowing the set of all them primes
let N be the greatest known prime and F(N) be the primal factorial of N (for instance if N is 5 than F(N) is 2 x 3 x 5 or if N is 11 then F(N) is 2 x 3 x 5 x 7 x 11) then for some prime g between 2 and N including 2 and N the g-th brotherhood of primes is B(g) = {F(N)/g x {k | (0<k<g)} (+/-) {all the elements of type g^n where n is natural and g^n is less than F(N)/g except if g=2 then n is natural and g^(n-1) is less than F(N)/g)}}.
THESIS: The union of all the brotherhoods B(g) for g prime between 2 and N including 2 and N is the set of ALL THE PRIMES AND PRIMES ALONE from 1 to F(N).
EXAMPLE: N = 5; F(N) = 2 x 3 x 5 = 30;
B(2) = {15 x {1} (+/-) {2^1, 2^2, 2^3, 2^4}} = {13, 17, 11, 19, 7, 23, 29, 1}
B(3) = {10 x {1, 2} (+/-) {3^1, 3^2}} = {7, 13, 1, 19, 17, 23, 11, 29}
B(5) = {6 x {1, 2, 3, 4} (+/-) {5^1}} = {1, 11, 7, 17, 13, 23, 19, 29}
it occurs that B(2) = B(3) = B(5) but that doesn't have to be the case for larger N; all the primes up to F(5)=30 are {2, 3, 5} U B(2) U B(3) U B(5) = {1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29}. Now the method may continue for N = 29 and F(N) = 6'469'693'230 it is some number between 30^6 and 30^7; 30 being F(5); which only speaks in favor of how fast this divergence in obtaining the unknown primes is. you'll check it out right...!?!
