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Jurkat-Richert Theorem

Number Theory

The Jurkat-Richert theorem is a result in sieve theory, proved by Wolfgang Jurkat and Hans-Egon Richert in 1965. It gives upper and lower bounds on how many integers in a finite sequence remain after integers divisible by a set of primes are sieved out, refining earlier sieve methods with tighter estimates built from multiplicative functions and a difference differential equation. The theorem became a key ingredient in later proofs about the distribution of primes, including Chen's theorem on Goldbach's conjecture. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/

Facts
Classification
Statement Form
Inequality 1
Proof Year
1965 1
Connections

Has Statement Form

Inequality, Concepts

Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.

Sources
1. Jurkat-Richert theorem (Wikipedia)
Introduction, second sentence
Quote, Introduction, second sentence
It was proved in 1965 by Wolfgang B. Jurkat and Hans-Egon Richert.
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