Quantum photon sources of high rate, brightness, and purity are increasingly desirable as quantum information systems are quickly scaled up and applied to many fields. Using a periodically poled lithium niobate microresonator on chip, we demonstrate photon-pair generation at high rates of 8.5 MHz and 36.3 MHz using only 3.4-$\mu$W and 13.4-$\mu$W pump power, respectively, marking orders of magnitude improvement over the state-of-the-art. The measured coincidence to accidental ratio is well above 100 at those high rates and reaches $14,682\pm 4427$ at a lower pump power. The same chip enables heralded single-photon generation at tens of megahertz rates, each with low auto-correlation $g^{(2)}_{H}(0)=0.008$ and $0.097$ for the microwatt pumps. Such distinct performance, facilitated by the chip device's noiseless and giant optical nonlinearity, will contribute to the forthcoming pervasive adoption of quantum optical information technologies.
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