The sum-free process

$S\subseteq {\mathbb{Z}}_{2n}$ is said to be sum-free if $S$ has no solution to the equation $a+b=c$. The sum-free process on ${\mathbb{Z}}_{2n}$ starts with $S:=\mathrm{\varnothing }$, and iteratively inserts elements of ${\mathbb{Z}}_{2n}$, where each inserted element is chosen uniformly at random from the set of all elements that could be inserted while maintaining that $S$ is sum-free. We prove a lower bound (which holds with high probability) on the final size of $S$, which matches a more general result of Bennett and Bohman, and also matches the order of a sharp threshold result proved by Balogh, Morris and Samotij. We also show that the set $S$ produced by the process has a particular non-pseudorandom property, which is in contrast with several known results about the random greedy independent set process on hypergraphs.