Using the latest observational data we obtain a lower bound on the initial value of the quintessence field in thawing quintessence models of dark energy. For potentials of the form V(phi) phi^{pm2} we find that the initial value |phi_i|>7x10^{18}gev. We then relate phi_i to the duration of inflation by assuming that the initial value of the quintessence field is determined by quantum fluctuations of the quintessence field during inflation. From the lower bound on $phi_i$ we obtain a lower bound on the number of e-foldings of inflation, namely, N>2x10^{11}. We obtain similar bounds for other power law potentials for which too we obtain |phi_{i}|>O(M_{P}.
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