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Using the latest observational data we obtain a lower bound on the initialvalue 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 byassuming that the initial value of the quintessence field is determined byquantum fluctuations of the quintessence field during inflation. From the lowerbound on $\phi_i$ we obtain a lower bound on the number of e-foldings ofinflation, namely, N>2x10^{11}. We obtain similar bounds for other power lawpotentials for which too we obtain |\phi_{i}|>O(M_{P}.

Thawing quintessence from the inflationary epoch to today