## More Properties in Goldbach’s Conjecture

**Authors:** C. G. Provatidis

This paper reveals that the reference function G(2n)=2n/(ln(n))^2 plays a significant role in the distribution of the total number of pairs (p, q) of primes that fulfill the condition (p + q = 2n), which constitutes Goldbach’s conjecture. Numerical experiments up to 2n=500,000 show that, in the plot of the number of pairs versus 2n, the ratio of the lowest points over G(2n) tends asymptotically to the value 2/3. The latter fact dictates that the lower bound concerning the minimum number of pairs that fulfill Goldbach’s conjecture is equal to 4n/[3(ln(n))^2]. Moreover, smoothed sequences by treatment of the aforementioned pairs are revealed.

**Comments:** 13 Pages.

**Download:** **PDF**

### Submission history

[v1] 2012-10-22 16:16:11

**Unique-IP document downloads:** 202 times

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.*

*
*