The Bombieri-Vinogradov Theorem bounds, on average over all moduli up to a given size, how evenly the prime numbers are distributed among the arithmetic progressions of each modulus, achieving on average a strength of estimate for that range of moduli that is not known to hold for any single modulus individually. Named for Enrico Bombieri and Askold Vinogradov, it functions in many applications as a substitute for the unproved Generalized Riemann Hypothesis and was a key ingredient in Yitang Zhang's work on bounded gaps between primes.
Facts
StatementThe Bombieri-Vinogradov theorem bounds, on average over moduli up to about the square root of x, how far the count of primes in arithmetic progressions can stray from its expected value, a result nearly as strong on average as the generalized Riemann hypothesis would give for one modulus at a time. 1 Classification
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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.
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Source Bombieri-Vinogradov Theorem (Wikipedia)
Sources
1. Bombieri-Vinogradov Theorem (Wikipedia)
Wikimedia Foundationlead paragraph, first sentence
the Bombieri-Vinogradov theorem (sometimes simply called Bombieri's theorem) is a major result of analytic number theory, obtained in the mid-1960s, concerning the distribution of primes in arithmetic progressions, averaged over a range of moduli.
lead paragraph, third sentence naming the 1965 publication
The Bombieri-Vinogradov theorem is named after Enrico Bombieri and A. I. Vinogradov, who published on a related topic, the density hypothesis, in 1965.
In Branch: Analytic Number Theory, Lead sentence
y called Bombieri's theorem) is a major result of analytic number theory, obtained in the mid-1960s, concerning the distribution o
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