  Formation of primordial black holes from inflationary fluctuations is
accompanied by a scalar induced gravitational wave background. We perform a
Bayesian search of such background in the data from Advanced LIGO and Virgo's
first, second and third observing runs, parametrizing the peak in the curvature
power spectrum by a log-normal distribution. The search shows no evidence for
such a background. We place 95\% confidence level upper limits on the
integrated power of the curvature power spectrum peak which, for a narrow
width, reaches down to $0.02$ at $10^{17}\,{\rm Mpc}^{-1}$. The resulting
constraints are stronger than those arising from BBN or CMB observations. In
addition, we find that LIGO and Virgo, at its design sensitivity, and the
Einstein Telescope can compete with the constraints related to the abundance of
the formed primordial black holes.
