This paper investigates the constraints on the amplitude of the primordial curvature power spectrum (PSP) and the abundance of primordial black holes (PBHs) based on pulsar timing array (PTA) observations. The study shows that significant PSP perturbations, necessary to seed a population of PBHs, can generate a scalar-induced gravitational wave (SIGW) signal detectable by PTA. The authors derive conservative bounds on the amplitude of the scalar power spectrum at PTA frequencies and estimate the resulting constraints on PBH abundance. They find that only a small fraction of dark matter can consist of stellar mass PBHs when calculated using threshold statistics. The strength and shape of the constraints depend on the power spectrum and the nature of non-Gaussianities. Constraints on PBH abundance are strongest in the mass range 0.1–10³ M☉, with the sub-solar mass range constrained only for narrow power spectra. These constraints are softened with positive non-Gaussianity and can be eliminated when f_NL > 5. In contrast, using the peaks theory approach relaxes the PTA constraints on PBHs, highlighting theoretical uncertainties in assessing PBH abundance. The study also discusses how strong positive non-Gaussianities can allow for heavy PBHs to potentially seed supermassive black holes (SMBHs). The paper emphasizes the importance of considering different power spectrum shapes and non-Gaussianity parameters in assessing PBH abundance and their implications for early universe cosmology.This paper investigates the constraints on the amplitude of the primordial curvature power spectrum (PSP) and the abundance of primordial black holes (PBHs) based on pulsar timing array (PTA) observations. The study shows that significant PSP perturbations, necessary to seed a population of PBHs, can generate a scalar-induced gravitational wave (SIGW) signal detectable by PTA. The authors derive conservative bounds on the amplitude of the scalar power spectrum at PTA frequencies and estimate the resulting constraints on PBH abundance. They find that only a small fraction of dark matter can consist of stellar mass PBHs when calculated using threshold statistics. The strength and shape of the constraints depend on the power spectrum and the nature of non-Gaussianities. Constraints on PBH abundance are strongest in the mass range 0.1–10³ M☉, with the sub-solar mass range constrained only for narrow power spectra. These constraints are softened with positive non-Gaussianity and can be eliminated when f_NL > 5. In contrast, using the peaks theory approach relaxes the PTA constraints on PBHs, highlighting theoretical uncertainties in assessing PBH abundance. The study also discusses how strong positive non-Gaussianities can allow for heavy PBHs to potentially seed supermassive black holes (SMBHs). The paper emphasizes the importance of considering different power spectrum shapes and non-Gaussianity parameters in assessing PBH abundance and their implications for early universe cosmology.