Direct numerical simulations (DNSs) of fully developed turbulent pipe flows with a 30R streamwise domain for Re-tau = 180, 544 and 934 were performed to see the turbulence statistics and the interactions between the near-wall and outer regions. There are some slight discrepancies between previous DNS data for turbulent pipe flows with low Reynolds numbers Re-tau approximate to 180 and the present data. These discrepancies arise because DNS results are sensitive to numerical conditions such as grid resolution and distribution. Our DNS data for various Reynolds numbers show that the near-wall peak in the streamwise turbulence intensity increases with increasing the Reynolds number. Evidence to support this finding was found in pre-multiplied energy spectra and the two-point amplitude modulation (AM) covariance. It was determined that both the long wavelength energy near the wall and the non-linear effects of AM contribute to the growth of the near-wall peak in the streamwise Reynolds stress.