Abstract: ATLAS has measured two-particle correlations as a function of the relative azimuthal angle, Delta phi, and pseudorapidity, Delta eta, in root s = 13 and 2.76 TeV pp collisions at the LHC using charged particles measured in the pseudorapidity interval vertical bar eta vertical bar < 2.5. The correlation functions evaluated in different intervals of measured charged-particle multiplicity show a multiplicity-dependent enhancement at Delta phi similar to 0 that extends over a wide range of Delta eta, which has been referred to as the “ridge.” Per-trigger-particle yields, Y(Delta phi) are measured over 2 < vertical bar Delta eta vertical bar < 5. For both collision energies, the Y(Delta phi) distribution in all multiplicity intervals is found to be consistent with a linear combination of the per-trigger-particle yields measured in collisions with less than 2 phi reconstructed tracks, and a constant combinatoric contribution modulated by cos (2 Delta phi). The fitted Fourier coefficient, nu(2,2), exhibits factorization, suggesting that the ridge results from per-event cos (2 phi) modulation of the single-particle distribution with Fourier coefficients nu(2). The nu(2) values are presented as a function of multiplicity and transverse momentum. They are found to be approximately constant as a function of multiplicity and to have a p(T) dependence similar to that measured in p + Pb and Pb + Pb collisions. The nu(2) values in the 13 and 2.76 TeV data are consistent within uncertainties. These results suggest that the ridge in pp collisions arises from the same or similar underlying physics as observed in p + Pb collisions, and that the dynamics responsible for the ridge has no strong root s dependence.