We perform a search for binary black hole mergers with one subsolar mass black hole and a primary component above $2 M_odot$ in the second observing run of LIGO/Virgo. Our analysis therefore extends previous searches into a mass region motivated by the presence of a peak in any broad mass distribution of primordial black holes (PBHs) around $[2-3] M_odot$ coming from the equation of state reduction at the QCD transition. Four candidate events are found passing a false alarm rate (FAR) threshold of 2 per year, although none are statistically significant enough for being clear detections. We first derive model independent limits on the PBH merging rates assuming a null result of the search. Then we confront them to two recent scenarios in which PBHs can constitute up to the totality of the Dark Matter, explain LIGO/Virgo mergers and the possible observation of a stochastic gravitational-wave background by NANOGrav. We find that these models still pass the rate limits and conclude that the analysis of the O3 and O4 observing runs will be decisive to test the hypothesis of a primordial origin of black hole mergers.
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