Some Conclusions About the Generalized Primes-twin and Others

Basing on Chebyshev inequality and on the computation of average concentration of all related subsets, the authors put forward and proved the following lemma, theorem, and the four corollaries: Lemma 1 There exists at least one of the sets of generalized prime-twins (namely one subset of the set of 2-primes group), which is an infinite set. Theorem 1 All the sets of generalized prime-twins or infinitely many ones among these sets are infinite sets. Corollary 1 There exists at least one of the sets of primes-triplet (namely one subset of the set of 3-primes-group), which is an infinite set. Corollary 2 All the sets of primes-triplet or infinitely many ones among these sets are infinite sets. Corollary 3 There exists at least one of the sets of h-primes-tuplet (namely one subset of the set of h-primes-group) which is an infinite set, where h is an inte ger≥2. Corollary 4 All the sets of h-primes-tuplet or infinitely many ones among these sets are infinite sets, where h is an integer≥2.