Farkas's pure-resolution conjecture for nonspecial curves

Let $p$ be an integer, and consider general smooth normal curves in projective space with the indicated genus and degree.

Farkas's conjecture. A general smooth normal curve $C\subset\mathbb P^r$ of odd genus $g=2p+3$ and degree $d=2g$ has a pure resolution, equivalently satisfies $N_p$. A general smooth normal curve of even genus $g=2p+6$ and degree $2g-2$ has a pure resolution, equivalently satisfies $N_p$.

The supplied status evidence says that this case was settled in the cited work using reducible curves, so the conjecture is recorded as solved.