Graduate Using Statistics to Test for Normality of Pi

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Testing the normality of π involves assessing whether each digit appears with equal frequency, and one suggested method is to randomly sample strings of size 20 and analyze the frequencies using a chi-squared test. This approach is deemed sound for evaluating uniform distribution among the digits. There is a question about whether normality is dependent on the numeral base, as patterns may emerge in one base that appear random in another. Research indicates that π has shown normality up to 22.5 trillion decimal places in base 10 and an equivalent amount in hexadecimal. The discussion highlights the importance of statistical methods in understanding the distribution of digits in π.
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Is there a " reasonable" way to test for the normality of ##\pi## , i .e., that every digit occurs with the same frequency? Someone suggested randomly sampling strings of size 20 and outputting the frequency. Then I guess we could average the frequencies among samples , use a chi-squared test. Assuming random sampling can be done, is this a sound way of testing?
 
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Yes. The Chi-squared goodness of fit test can be used to test if the digits are from a uniform distribution.
 
Is normality dependent upon the base - is it possible for there to be a pattern in one base that then appears random in another?

anyway, here is one method that showed normality out to 22.5 trillion base 10 decimal places and an equivalent number of hexideximal ones

https://arxiv.org/pdf/1612.00489.pdf
 

Thread 'Two interesting number theory tricks'

First trick I learned this one a long time ago and have used it to entertain and amuse young kids. Ask your friend to write down a three-digit number without showing it to you. Then ask him or her to rearrange the digits to form a new three-digit number. After that, write whichever is the larger number above the other number, and then subtract the smaller from the larger, making sure that you don't see any of the numbers. Then ask the young "victim" to tell you any two of the digits of the...
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