Mary has a sequence m_2, m_3, m_4, . . . , such that for each b \ge 2, m_b is the least positive integer m for which none of the base-b logarithms \log_b{(m)}, \log_b{(m + 1)}, . . . , \log_b{(m + 2017)} are integers. Find the largest number in her sequence.
Source: HMMT November, Theme Round, 2017
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