Using ALMA observations, we performed the first systematic survey for transient brightenings (i.e. weak, small-scale episodes of energy release) in the quiet solar chromosphere at 3 mm. Our dataset included images of six 87 x 87 regions of the quiet Sun obtained with angular resolution of a few arcsec at a cadence of 2 s. The transient brightenings were detected as weak enhancements above the average intensity after we removed the effect of the p-mode oscillations. A similar analysis, over the same regions, was performed for simultaneous 304 and 1600 AA data obtained with the Atmospheric Imaging Assembly. We detected 184 3 mm transient brightening events with brightness temperatures from 70 K to more than 500 K above backgrounds of $sim 7200-7450$ K. Their mean duration and maximum area were 51.1 s and 12.3 Mm$^2$, respectively, with a weak preference of appearing at network boundaries rather than in cell interiors. Both parameters exhibited power-law behavior with indices of 2.35 and 2.71, respectively. Only a small fraction of ALMA events had either 304 or 1600 AA counterparts but the properties of these events were not significantly different from those of the general population except that they lacked their low-end energy values. The total thermal energies of the ALMA transient brightenings were between $1.5 times 10^{24}$ and $9.9 times 10^{25}$ erg and their frequency distribution versus energy was a power law with an index of 1.67. We found that the power per unit area provided by the ALMA events could account for only 1% of the chromospheric radiative losses (10% of the coronal ones). Therefore, their energy budget falls short of meeting the requirements for the heating of the upper layers of the solar atmosphere and this conclusion does not change even if we use the least restrictive criteria possible for the detection of transient brightenings.
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