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What is the best lower bound for the longest interval contained in $[1,x]$ free of primes and products of two primes? In other words I am asking for the best lower bounds in a variant of the Westzynthius-Erdos-Rankin problem of finding large gaps between primes, as in this recent paper.

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  • $\begingroup$ A trivial bound is $\log x/\log\log x.$ $\endgroup$
    – Charles
    Mar 14, 2016 at 19:52

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