What is recorded here?
Proved that the prime numbers contain arithmetic progressions of every finite length, using a transference principle that imports dense-set results into a suitable pseudorandom majorant for the primes.
Source-linked catalogue note. A detailed explanatory guide has not yet been prepared for this entry.
Scientific scope
The record is the exact two-author Annals paper. Szemerédi’s theorem, Goldston–Yıldırım estimates, later quantitative improvements and broader linear-equations-in-primes results retain separate attribution.
Read the original work
- Annals of Mathematics, The primes contain arbitrarily long arithmetic progressions
- Green and Tao, prime progressions full paper
This English explanation is an editorial reading view. It does not replace the complete original work or certify its science.
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People and systems
Ben Green; Terence Tao
The named authors contributed to this scoped work; individual effort shares and later applications are not assigned by the byline.
Research locations and affiliations
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Documented countries / regions: United Kingdom, United States
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English catalogue narrative
Green and Tao: arbitrarily long arithmetic progressions of primes
Proved that the prime numbers contain arithmetic progressions of every finite length, using a transference principle that imports dense-set results into a suitable pseudorandom majorant for the primes.
Scientific scope
The record is the exact two-author Annals paper. Szemerédi’s theorem, Goldston–Yıldırım estimates, later quantitative improvements and broader linear-equations-in-primes results retain separate attribution.
Reading status
This is a source-linked WRS catalogue note. A full explanatory guide and independent scientific reconstruction have not been completed for this entry. Read the identified original work for its complete narrative and arguments.
People and systems
Ben Green; Terence Tao
The named authors contributed to this scoped work; individual effort shares and later applications are not assigned by the byline.