The Copeland-Erdős constant is not strongly normal in base 10
No: the Copeland-Erdős constant is not simply strongly normal in base 10, hence not strongly normal in base 10, and the failure is already visible in the digit 0. The proof compares the zero count at two positions in the expansion. Every prime in [10^(6n), 10^(6n) + 10^(5n)) begins with 1 followed by n zeros, and Ingham's 1937 short-interval theorem with exponent 5/6 supplies about 10^(5n)/(6n log 10) such primes, so the zero excess across that stretch is of order 10^(5n), while simple strong normality would cap the discrepancy at O(sqrt(N log log N)) with N of order 10^(6n), that is at order 10^(3n). Belshaw and Borwein's 2013 Champernowne argument is the model; Ingham replaces the trivial prime count. Strong normality in other bases is not addressed.
Exact FrontierDelta
Scope and record
Occurred: Sep 13, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: lean-checked. Publication: preprint. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.
Canonical aliases: The Copeland-Erdős constant is not strongly normal in base 10 · Copeland-Erdős not strongly normal
Confidence: Not scored
Registry verification: lean checked · preprint · resolved
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VibeMathed
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ChatGPT-6 Astra
model · ai model contributor · OpenAI
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VibeMathed record: The Copeland-Erdős constant is not strongly normal in base 10 evidence for this event
This event attributed to ChatGPT-6 Astra
The Copeland-Erdős constant is not strongly normal in base 10 parent of this event
Belshaw's thesis, section 4.7, where the question is asked evidence for this event
Catt, Coons and Velich (2016), section 3: "of this we have no proof" evidence for this event
No: the Copeland-Erdős constant is not simply strongly normal in base 10, hence not strongly normal in base 10, and the failure is already visible in the digit 0. The proof compares the zero count at two positions in the expansion. Every prime in [10^(6n), 10^(6n) + 10^(5n)) begins with 1 followed by n zeros, and Ingham's 1937 short-interval theorem with exponent 5/6 supplies about 10^(5n)/(6n log 10) such primes, so the zero excess across that stretch is of order 10^(5n), while simple strong normality would cap the discrepancy at O(sqrt(N log log N)) with N of order 10^(6n), that is at order 10^(3n). Belshaw and Borwein's 2013 Champernowne argument is the model; Ingham replaces the trivial prime count. Strong normality in other bases is not addressed. parent of this event
Copeland–Erdős constant evidence for this event
The Copeland-Erdős constant is not strongly normal in base 10 evidence for this event
Ingham (1937), the one external theorem evidence for this event
GitHub Actions build printing the final theorems and axioms evidence for this event
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