Sampling Goldbach Numbers at Random

2015/08/05 by Ljuben Mutafchiev, Mutafchiev, Ljuben
Mathematics · #05A17 #11P32 #60C05 #Analytic Number Theory Research #Benford’s Law and Fraud Detection #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #Probability (math.PR) #Random Matrices and Applications #math.CO #math.NT #math.PR #msc:05A17 #msc:11P32 #msc:60C05

paper · pdf · doi:10.48550/arxiv.1508.04457

arxiv created 2015/08/05 · openalex publication_date 2015/08/05 · arxiv updated 2015/08/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let Σ_2n be the set of all partitions of the even integers from the interval (4,2n], n>2, into two odd prime parts. We select a partition from the set Σ_2n uniformly at random. Let 2G_n be the number partitioned by this selection. 2G_n is sometimes called a Goldbach number. In [6] we showed that G_n/n converges weakly to the maximum T of two random variables which are independent copies of a uniformly distributed random variable in the interval (0,1). In this note we show that the mean and the variance of G_n/n tend to the mean μ_T=2/3 and variance σ_T²=1/18 of T, respectively. Our method of proof is based on generating functions and on a Tauberian theorem due to Hardy-Littlewood-Karamata.

Citations

• On some problems of a statistical group-theory. IV

Related

• On the Distribution of the Number of Goldbach Partitions of a Randomly Chosen Positive Even Integer
• A Note on Goldbach Partitions of Large Even Integers
• On Randomness of Goldbach Sequences
• Goldbach Conjecture: Violation Probability and Generalization to Prime-like Distributions
• On Partitions of Goldbach's Conjecture