Very thin silver nanowires are ideal building blocks for fabricating high-performance transparent conductive films simultaneously with low sheet resistance, high visible light transparency, a small haze factor, and high uniformity. Synthesis of very thin silver nanowires with an average diameter close to 20 nm has been realized by a polyol reduction method in the presence of Br- and Cl- ions. However, nanoparticles contained in the product are detrimental to the overall performance of transparent conductive films, and there have been no methods to purify very thin silver nanowires which are both cost-effective and environmentally friendly. In this work, we report on the Ostwald ripening-driven coarsening of the nanoparticles, followed by sedimentation and brief filtration to separate the particles from very thin silver nanowires. This method is free from the involvement of toxic acetone and could produce very thin silver nanowires with high purity. It is convenient and suitable for large-scale implementation. The films prepared with the purified very thin silver nanowires exhibit a low sheet resistance of 71.3 +/- 2.9 (-1) at a high transmittance of 91.7%, a low haze of 1.0%, and a small standard deviation of the sheet resistance of 4.0%, without further treatment processes. The findings in this work will pave the way for the real-world application of very thin silver nanowires towards high-performance transparent conductive films and flexible electronics.