Divisor Goldbach Conjecture and its Partition Number

2016/03/14 by Yan Kun, Kun, Yan, Li Hou Biao +1
Mathematics · #11P32 (Primary) #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1603.05233

openalex publication_date 2016/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Based on the Goldbach conjecture and arithmetic fundamental theorem, the Goldbach conjecture was extended to more general situations, i.e., any positive integer can be written as summation of some specific prime numbers, which depends on the divisible factor of this integer, that is: For any positive integer n~(n>2), if there exists an integer m, such that m|n~( 1 < m < n ), then n=∑_i=1^m p_i , where p_i~(i=1,2 ,3...m) is prime number. In addition, for more prime summands, the combinatorial counting is also discussed. For some special cases, some brief proofs are given. By the use of computer, the preliminary numerical verification was given, there is no an anti-example to be found.

Citations

• Empirical verification of the even Goldbach conjecture and computation of prime gaps up to 4⋅10¹⁸

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