Sourceunknowntext stored

https://arxiv.org/html/math.NT/0508185

Author not recordedDate not recordedOriginal︎ ↗

Claims1

ExaminationsNone

Text56 sections

VersionsOne known

CopiesNone recorded

CorrectionsNone recorded

Facts checked Nov 9, 2026

ReachNo copies recorded

StructureIn 1 claim's map1 source downstream across 1 claim

Evidence1 reading · 1 read wholeSupports 1No claim cites an examination's findings

ReviewsNot reviewed

Stewards’ notes · 1

The level of distribution of the primes is known to be at least one half.
Supports. The Goldston–Pintz–Yıldırım paper gives the precise definition in use (the averaged estimate holds for moduli up to N to the power theta minus epsilon, for every epsilon) and states the Bombieri–Vinogradov theorem explicitly with its logarithmic saving, from which level one half follows directly under that definition. This is the primary technical statement of the claim in the small-gaps literature. Sep 16, 2026

Examinations

None recorded. An examination is commissioned by a claim’s Steward for what its claim rests on; a review of the document for its own sake is asked for as a request bearing on it.

Text767 passages · 1 marked

No examination yetMarked passage

Report GitHub Issue6 passages

Back to arXiv1 passage

Report Issue0 passages

Back to Abstract0 passages

Download PDF1 passage

1 Introduction0 passages

2 Approximating prime tuples0 passages

3 Proofs of Theorems 1 and 20 passages

4 Further Remarks on Section 30 passages

5 Two Lemmas0 passages

6 A special case of Proposition 10 passages

7 First Part of the Proof of Proposition 10 passages

8 Completion of the proof of Proposition 1: Evaluating an integral0 passages

9 Proof of Proposition 20 passages

10 Proof of Theorem 30 passages

References0 passages

License: Assumed arXiv.org perpetual non-exclusive license2 passages

D. A. Goldston1 passage

Email address: goldston@math.sjsu.edu2 passages

Email address: pintz@renyi.hu2 passages

Email address: yalciny@boun.edu.tr4 passages

1. Introduction28 passages · 1 marked

Elliott and Halberstam [ 5 ] conjectured that the primes have level of distribution 1. According to the Bombieri-Vinogradov theorem, the primes are known to have level of distribution 1 / 2 1/2 .

The level of distribution of the primes is known to be at least one half.VerifiedReading · this claim’s Steward

Supports. The Goldston–Pintz–Yıldırım paper gives the precise definition in use (the averaged estimate holds for moduli up to N to the power theta minus epsilon, for every epsilon) and states the Bombieri–Vinogradov theorem explicitly with its logarithmic saving, from which level one half follows directly under that definition. This is the primary technical statement of the claim in the small-gaps literature.

We have35 passages

2. Approximating prime tuples0 passages

Let65 passages

3. Proofs of Theorems 1 and 228 passages

To prove Theorem 2, we modify the previous proof by considering59 passages

4. Further Remarks on Section 325 passages

In ( 3.11 ) we chose11 passages

5. Two Lemmas52 passages

6. A special case of Proposition 13 passages

Supposing6 passages

Proof . We have51 passages

Finally, if p > U p>U13 passages

7. First Part of the Proof of Proposition 10 passages

Let27 passages

By ( 6.6 ), we have30 passages

8. Completion of the proof of Proposition 1: Evaluating an integral0 passages

Let9 passages

Suppose that26 passages

This completes the evaluation of I 0 I_{0} , and we conclude7 passages

It is not hard to prove that26 passages

In particular, we have27 passages

9. Proof of Proposition 210 passages

We prove the following stronger version of Proposition 2. Let61 passages

We now show that in all three cases12 passages

10. Proof of Theorem 323 passages

By Proposition 2 and ( 10.5 ) we have8 passages

We conclude, on introducing the parameters8 passages

Let17 passages

Furthermore, we choose5 passages

Thus, we see that2 passages

Let us choose now28 passages

References39 references

Instructions for reporting errors7 passages

Major funding support from0 passages

Lineage across 1 claim

Draws on · none recorded

This source

https://arxiv.org/html/math.NT/0508185

in 1 claim's map

Drawn on by · 1

Unheralded Mathematician Bridges the Prime Gap | Quanta MagazineunknownMay 19, 20131 claimRestates it faithfully, on 1 claim.

Record

Kind: unknown
Authors: Not recorded
Publisher: Not recorded
Published: Not recorded
DOI: None
Link: https://arxiv.org/html/math.NT/0508185
Archived copy: None found
Stored text: 135,426 characters, retrieved Sep 16, 2026 · 56 sections, 767 passages
Claims extracted: Not recorded
Versions: One known
Copies: None recorded
Corrections: None recorded
Facts checked: Nov 9, 2026

History 4

Nov 9, 2026DividedSegmenter · Divided into 823 parts by its own structure
Nov 9, 2026FactsFacts fetcher · Facts looked up
Sep 16, 2026ReadingSteward of “The level of distribution of the primes is know…” · supports, read whole
Sep 16, 2026Entered the graphEntered the graph; copy stored