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Dynamic spectrum allocation has proven promising for mitigating the spectrum scarcity problem. In this model, primary users lease chunks of under-utilized spectrum to secondary users, on a short-term basis. Primary users may need financial motivations to share spectrum, since they assume costs in obtaining spectrum licenses. Auctions are a natural revenue generating mechanism to apply. Recent design on spectrum auctions make the strong assumption that the primary user knows the probability distribution of user valuations. We study revenue-maximizing spectrum auctions in the more realistic prior-free setting, when information on user valuations is unavailable. A two-phase auction framework is constructed. In phase one, we design a strategyproof mechanism that computes a subset of users with an interference-free spectrum allocation, such that the potential revenue in the second phase is maximized. A tailored payment scheme ensures truthful bidding at this stage. The selected users then participate in phase two, where we design a randomized competitive auction and prove its strategyproofness through the argument of bid independence. Employing probabilistic techniques, we prove that our auction generates a revenue that is at least 1/3 of the optimal revenue, improving the best known ratio of 1/4 proven for similar settings.