Z-score is not a direct measure of statistical significance, which necessarily needs a correct interpretation of z-score or similar numbers. If my measurement of normally distributed random variable resulted in the z-score of 5.0, it can still occur by a slim (<0.000058%) but still pure chance. If we don't know the variable's distribution in advance, the chance can be as high as 4% per Chebyshev's inequality. You don't have any necessary interpretation to derive your conclusion to exclude such possibilities.<p>The only thing one can conclude from your claim is that, the first handful number of digits in pi can be very, very slightly compressed if you are somehow able to ignore the size of that classifier [1]. The algorithmic randomness however requires the classifier to be included, and there is no known self-contained program that is smaller than printing all digits in verbatim or computing them in the first place.<p>[1] By the way, this is not really surprising at all. In fact there are 5,001 (<i>not</i> 5,000) out of first 10,000 decimal digits of pi that are between 5 and 9, so it can be very, very slightly compressed in that way---of course after the decompressor excluded.