Systematic KMTNet Planetary Anomaly Search. IV. Complete Statistical
  Sample of 2019 Prime-Field Microlensing Planets
  We report the complete statistical planetary sample from the prime fields
($\Gamma \geq 2~{\rm hr}^{-1}$) of the 2019 Korea Microlensing Telescope
Network (KMTNet) microlensing survey. We develop the optimized KMTNet
AnomalyFinder algorithm and apply it to the 2019 KMTNet prime fields. We find a
total of 14 homogeneously selected planets and report the analysis of three
planetary events, KMT-2019-BLG-(1042,1552,2974). The planet-host mass ratios,
$q$, for the three planetary events are $6.34 \times 10^{-4}, 4.89 \times
10^{-3}$ and $6.18 \times 10^{-4}$, respectively. A Bayesian analysis indicates
the three planets are all cold giant planets beyond the snow line of their host
stars. The 14 planets are basically uniform in $\log q$ over the range $-5.0 <
\log q < -1.5$. This result suggests that the planets below $q_{\rm break} =
1.7 \times 10^{-4}$ proposed by the MOA-II survey may be more common than
previously believed. This work is an early component of a large project to
determine the KMTNet mass-ratio function, and the whole sample of 2016--2019
KMTNet events should contain about 120 planets.
