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Assuming that the common-spectrum process in the NANOGrav 12.5-year dataset has an origin of scalar-induced gravitational waves, we study the enhancement of primordial curvature perturbations and the mass function of primordial black holes, by performing the Bayesian parameter inference for the first time. We obtain lower limits on the spectral amplitude, i.e., <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">A</mi><mo>≳</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>2</mn></mrow></msup></mrow></semantics></math></inline-formula> at 95% confidence level, when assuming the power spectrum of primordial curvature perturbations to follow a log-normal distribution function with width <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>σ</mi></semantics></math></inline-formula>. In the case of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>σ</mi><mo>→</mo><mn>0</mn></mrow></semantics></math></inline-formula>, we find that the primordial black holes with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup><mo>−</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>2</mn></mrow></msup></mrow></semantics></math></inline-formula> solar mass are allowed to compose at least a fraction <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mn>10</mn><mrow><mo>−</mo><mn>6</mn></mrow></msup></semantics></math></inline-formula> of dark matter. Such a mass range is shifted to more massive regimes for larger values of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>σ</mi></semantics></math></inline-formula>, e.g., to a regime of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>4</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup><mo>−</mo><mn>0.2</mn></mrow></semantics></math></inline-formula> solar mass in the case of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>σ</mi><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula>. We expect the planned gravitational-wave experiments to have their best sensitivity to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">A</mi></semantics></math></inline-formula> in the range of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup></semantics></math></inline-formula> to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mn>10</mn><mrow><mo>−</mo><mn>7</mn></mrow></msup></semantics></math></inline-formula>, depending on the experimental setups. With this level of sensitivity, we can search for primordial black holes throughout the entire parameter space, especially in the mass range of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mn>10</mn><mrow><mo>−</mo><mn>16</mn></mrow></msup></semantics></math></inline-formula> to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mn>10</mn><mrow><mo>−</mo><mn>11</mn></mrow></msup></semantics></math></inline-formula> solar masses, where they could account for all dark matter. In addition, the importance of multi-band detector networks is emphasized to accomplish our theoretical expectation.