AWhat changed
Factorial/prime-power identities yield rigorous weighted-prime bounds and an all-admissible-integer Bertrand proof with explicit analytic/finite-case separation.
Scientific scope
Factorial/prime-power identities yield rigorous weighted-prime bounds and an all-admissible-integer Bertrand proof with explicit analytic/finite-case separation. The target is quantitative upper/lower weighted-prime and interval-count bounds and the original Bertrand proof for integer a>3: a prime lies strictly between a and 2 a−2. Original 381–382 treats a>160 analytically and smaller admissible integers by prime tables; finite table checks alone do not prove the infinite range. Theta sums natural logarithms over primes up to x, distinct from the auxiliary prime-power sum. These bounds do not prove pi(x)~x/log(x), a zero-free zeta theorem or general primes in every shorter interval. Later series applications impose positivity/monotonicity conditions and are not advertised here as universal convergence criteria. no independent full proof replay. Presentation 1850 and publication 1852 are distinguished without duplicate counting.
Evidence
Source-linked, scoped account of the original work. The published scope states the scientific assumptions and remaining verification limits. WRS has not independently certified the full proof, experimental result or system benchmark.
Contributors
- Tchebichef (Chebyshev) · SCIENCE: Original source-listed scientific author of this scoped work; byline does not determine effort fractions.
- Tchebichef, Mémoire sur les nombres premiers (1852), original 366–390
- Numdam/Bn F Mathdoc catalogue of the 1852 Tchebichef memoir
Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.
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