The yet to be verified proof of Harald Helfgott of this conjecture verifies the GRH for several thousand small characters up to a certain imaginary part to obtain sufficient bounds that prove the conjecture for all integers above 1029, integers below which have already been verified by brute force.
Bernhard Riemann | Riemann zeta function | Riemann surface | Riemann hypothesis | Alvarez hypothesis | Witch-cult hypothesis | extraterrestrial hypothesis | two-source hypothesis | Riemann sphere | Generalized System of Preferences | Riemann solver | Riemann-Roch theorem | Rare Earth hypothesis | Hugo Riemann | Hebrew Gospel hypothesis | Generalized linear model | Articulata hypothesis | Warburg hypothesis | Two-source hypothesis | Turnover-pulse hypothesis | Three-source hypothesis | Swoon hypothesis | Stolen body hypothesis | Statistical hypothesis testing | Schinzel's hypothesis H | Riemann Xi function | Riemann's function | Riemann's existence theorem | Riemann–Roch theorem | Riemann manifold |
Deshouillers, Effinger, te Riele and Zinoviev conditionally proved the weak conjecture under the GRH.
In 1997 Deshouillers, Effinger, te Riele, and Zinoviev showed that the generalized Riemann hypothesis implies that every odd number greater than 5 is the sum of three primes.