Systematic KMTNet Planetary Anomaly Search. XIII. Complete Sample of 2021 Prime Field Planets

The Systematic KMTNet Planetary Anomaly Search series was conducted using the KMTNet data archived from $2016$ to $2019$. From this first phase of the series, we reported a total of $50$ planetary systems hidden in the data archive, which represent about $35\%$ of the total microlensing planets discovered from $2016$ to $2019$, demonstrating that this semi-machine-based search is a crucial channel for building a complete microlensing planet sample. We continue this series for $2021$ and beyond to expand the microlensing planet sample. In this work for the $2021$ KMTNet high-cadence fields (Prime fields), we find seven hidden planetary systems and three planet candidates. These new planets represent about $33\%$ of the total microlensing planets discovered within the Prime fields observed during the $2021$ bulge season. While the by-eye search is the primary channel for detecting microlensing planets (i.e., two-thirds of microlensing planet discoveries), this work clearly shows that a systematic search series is still necessary for constructing a complete microlensing planet sample. Such a sample is essential for conducting unbiased statistical studies of planet demographics in our Galaxy. Datasets for all the events used for analyses in this work are publicly available.