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Measuring the size of the Internet via Monte Carlo sampling requires probing a large portion of the Internet protocol (IP) address space to obtain an accurate estimate. However, the distribution of information servers on the Internet is highly nonuniform over the IP address space. This allows us to design probing strategies based on importance sampling for measuring the prevalence of an information service on the Internet that are significantly more effective than strategies relying on Monte Carlo sampling. We present thorough analysis of our strategies together with accurate estimates for the current size of the Internet Protocol Version 4 (IPv4) Internet as measured by the number of publicly accessible web servers and FTP servers.