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Considering the (infinite) set of all positive integers that are a product of $2$ primes only, represented in binary $100...01$.

Question: is the distribution of the proportion of $0,1$ digits "uniform" (meaning $Pr(0) = Pr(1)$) ? Or should we expect an asymmetric distribution (eg. the relative frequency of "$1$"s to exceed that of the "$0$"s) ?

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    @Brian M. Scott Yes, essentially that is it. (But maybe that is a bit too strong: it would be enough if the limit holds with probability$1$or with probability converging to 1. So an asymptotically almost sure (a.a.s) or a probability convergence or any other form of weaker convergence would also be interesting). Thanks a lot for a clearer formulation.2012-12-30

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