AI-reported failure of strong normality for the Copeland–Erdős constant
- Mathematics
The decimal Copeland–Erdős constant formed by concatenating the primes is not simply strongly normal in base 10, and therefore is not strongly normal in base 10.
AI-reported failure of strong normality for the Copeland–Erdős constant
- Mathematics
The decimal Copeland–Erdős constant formed by concatenating the primes is not simply strongly normal in base 10, and therefore is not strongly normal in base 10.
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Understand the problem ↓Understanding the problem
Read the background
The decimal Copeland–Erdős constant formed by concatenating the primes is not simply strongly normal in base 10, and therefore is not strongly normal in base 10.
Why it matters
If correct, answers a named question about the fluctuation of digits in a classical normal constant.
What counts as progress
The Copeland-Erdős constant $0.235711131719\ldots$ concatenates the primes in increasing order; Copeland and Erdős proved in 1946 that it is normal in base 10. Strong normality, introduced by Belshaw and Borwein, also prescribes the size of the digit-count fluctuations: $x$ is simply strongly normal in base $b$ if for every digit the discrepancy $Z_d(x;N) - N/b$ has $\limsup$ and $\liminf$ equal to $\pm\sqrt{b-1}/b$ on the scale $\sqrt{2N\log\log N}$, and strongly normal if this holds in every base $b^k$. Champernowne's number is normal but not strongly normal. Does the Copeland-Erdős concatenation of the primes also fail to be strongly normal in base 10?
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AI-reported failure of strong normality for the Copeland–Erdős constant