# The Ternary Goldbach Conjecture

Master's dissertation in mathematics, 2020

Cite as: Luke Collins. (2020). The Ternary Goldbach Conjecture, Master's dissertation, University of Warwick.

## Abstract

We review Hardy–Littlewood's proof of the ternary Goldbach conjecture for sufficiently large odd numbers which assumes the Generalised Riemann Hypothesis, then discuss Vinogradov's improvement of the minor arcs bound to prove the result unconditionally for $N$ sufficiently large (i.e., Vinogradov's theorem), and finally explore some ideas from Helfgott's 2014 proof which substantially improves the minor arc bounds, establishing the result analytically for $N\geqslant 10^{27}$, and checking the remaining cases by computer, proving the conjecture for all $N\geqslant 7$.