Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6423631 | Electronic Notes in Discrete Mathematics | 2016 | 6 Pages |
Abstract
Let P={p1;p2;â¦} 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/(12logâ¡n)2 converges weakly, as nââ, to a uniformly distributed random variable in the interval (0,1). The method of proof uses sizebiasing and the Laplace transform continuity theorem.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Ljuben Mutafchiev,