# The Goldbach problem

@inproceedings{Iwaniec2004TheGP, title={The Goldbach problem}, author={Henryk Iwaniec and Emmanuel Kowalski}, year={2004} }

This is a project for a student who likes problems about the distribution of prime numbers and who enjoyed the last part of the undergraduate course Analytic Number Theory related to the representation of every large enough positive integer as the sum of nine positive integer cubes. One of the most well-known open problems in all of mathematics is the Goldbach conjecture: every even integer greater than two is the sum of two primes. If true, it implies that every odd integer greater than five… Expand

#### 28 Citations

The ternary Goldbach problem

- Mathematics
- 2014

The ternary Goldbach conjecture, or three-primes problem, states that every odd number n greater than 5 can be written as the sum of three primes. The conjecture, posed in 1742, remained unsolved… Expand

The ternary Goldbach conjecture is true

- Mathematics
- 2013

The ternary Goldbach conjecture, or three-primes problem, asserts that every odd integer $n$ greater than $5$ is the sum of three primes. The present paper proves this conjecture.
Both the ternary… Expand

Minor arcs for Goldbach's problem

- Mathematics
- 2012

The ternary Goldbach conjecture states that every odd number n>=7 is the sum of three primes. The estimation of sums of the form \sum_{p\leq x} e(\alpha p), \alpha = a/q + O(1/q^2), has been a… Expand

A Rigorous Proof for the Strong Goldbach Conjecture

- Computer Science
- 2016

It is shown that it is always possible to find at least one pair of prime numbers according to the former two expressions for any given even number greater or equal to 6. Expand

Major arcs for Goldbach's problem

- Mathematics
- 2013

The ternary Goldbach conjecture, or three-primes problem, asserts that every odd integer n greater than 5 is the sum of three primes. The present paper proves this conjecture. Both the ternary… Expand

eu AN EXPLORATION ON GOLDBACH ’ S CONJECTURE

- 2013

This paper divides the set of natural numbers in six equivalence classes and determines two of them as candidate to include all prime numbers. Concerning the even numbers themselves, these were… Expand

Some Considerations in Favor of the Truth of Goldbach's Conjecture

- Mathematics
- 2012

This article presents some considerations about the Goldbach's conjecture (GC). The work is based on analytic results of the number theory and it provides a constructive method that permits, given an… Expand

Explicit Estimates in the Theory of Prime Numbers

- Mathematics
- 2016

It is the purpose of this thesis to enunciate and prove a collection of explicit results in the theory of prime numbers.
First, the problem of primes in short intervals is considered. We prove that… Expand

On the existence of a non-zero lower bound for the number of Goldbach partitions of an even integer

- Mathematics, Computer Science
- Int. J. Math. Math. Sci.
- 2004

It will be shown how to determine by the method of induction the existence of a non-zero lower bound for the number of Goldbach partitions of all even integers greater than or equal to 4. Expand

Some Issues on Goldbach Conjecture

- Mathematics
- 2012

This paper presents a deterministic process of finding all pairs (p,q) of odd numbers (composites and primes) of natural numbers ≥ 3 whose sum (p + q) is equal to a given even natural number 2n ≥ 6.… Expand

#### References

Multiplicative Number Theory

- Mathematics
- 1967

From the contents: Primes in Arithmetic Progression.- Gauss' Sum.- Cyclotomy.- Primes in Arithmetic Progression: The General Modulus.- Primitive Characters.- Dirichlet's Class Number Formula.- The… Expand