Article ID Journal Published Year Pages File Type
6423631 Electronic Notes in Discrete Mathematics 2016 6 Pages PDF
Abstract

Let P={p1;p2;…} be the set of all odd primes arranged in increasing order. A Goldbach partition of the even integer 2k>4 is a way of writing it as a sum of two primes from P without regard to order. Let Q(2k) be the number of all Goldbach partitions of the number 2k. Assume that 2k is selected uniformly at random from the interval (4,2n], n>2, and let Yn=Q(2k) with probability 1=(n/2). We prove that the random variable Ynn/(12log⁡n)2 converges weakly, as n→∞, to a uniformly distributed random variable in the interval (0,1). The method of proof uses sizebiasing and the Laplace transform continuity theorem.

Related Topics
Physical Sciences and Engineering Mathematics Discrete Mathematics and Combinatorics
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