关于广义孪生素数的几个结论

基于Chebyshev不等式以及对所有相关子集平均浓度的计算,提出并证明了下列引理、定理,以及4条推论:引理1]至少有1个广义孪生素数集合(或称2素数组子集)是无限集合;定理1]全部的或无限多的广义孪生素数集合是无限集合;推论1]至少有1个3生素数集合(或称3素数组子集)是无限集合;推论2]全部的或无限多的3生素数集合是无限集合;推论3]普遍地说,至少有1个h生素数集合(或称h素数组子集)是无限集合(h是≥2的整数);推论4]普遍地说,全部的或无限多的h生素数集合是无限集合(h是≥2的整数)．

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.