Digit Frequencies in the Copeland-Erdos Constant

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

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


Snapshots


Details

detailSectionParagraph


Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send