Digit Frequencies in the Copeland-Erdos Constant

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In base 10, the Copeland–Erdos constant 0.23571113171923… is obtained by concatenating the digits of the primes 2, 3, 5, … . Copeland and Erdos proved that this constant is normal in base 10, meaning that in the limit the frequency of each digit is , the frequency of each block of two digits is , and so on. The sizes of the pie chart slices show the frequencies of single digits for a given approximation. As more primes are used the slices become more nearly equal, reflecting the constant's statistical normality. No proof of normality is known for this number in other bases.

Contributed by: Hector Zenil (March 2011)
Open content licensed under CC BY-NC-SA




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