Recently Sarkar (DCC 2014) has proposed a new attack on small decryption exponent when RSA Modulus is of the form N=prq for r≥2. This variant is known as Prime Power RSA. The work of Sarkar improves the result of May (PKC 2004) when r≤5. In this paper, we improve the work of Sarkar when 2<r≤8. We also study partial key exposure attack on Prime Power RSA. Our result improves the works of May (PKC 2004) when r≤8 and the decryption exponent d<N1r+1+3r-23r+3+33(r+1). © 2016 Elsevier B.V. All rights reserved.