Theorem

Vinogradov's Theorem

Number Theory

Every sufficiently large odd integer can be written as the sum of three prime numbers. Proved by Ivan Vinogradov using the Hardy-Littlewood circle method, it established the weak Goldbach conjecture for all large enough odd numbers.

Facts

Statement

Every sufficiently large odd integer can be expressed as the sum of three prime numbers. 1

Proof Year

1937 1

The lead section dates the result broadly to the 1930s; the strategy-of-proof section gives the specific year 1937 for Vinogradov's unconditional bound completing the proof.

Classification

Statement Form

Existence Theorem 1

Connections

Source Vinogradov's Theorem (Wikipedia)

Sources

1. Vinogradov's Theorem (Wikipedia)

Wikimedia Foundation

Lead section, opening definition
Vinogradov's theorem is a result which implies that any sufficiently large odd integer can be written as a sum of three prime numbers.
Strategy of proof section, sentence dating the unconditional bound to 1937
In 1937 Vinogradov gave an unconditional upper bound for |S(α)|.
Proved By: Ivan Vinogradov, Lead
It is named after Ivan Matveyevich Vinogradov, who proved it in the 1930s.

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Vinogradov's Theorem

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