Source · Reference

OpenMath · prime note

Reading source record a640f3adfa536da0. View default cited record →

Overview

Elementary-number-theory reference prose

Passages

The exact passages cited in OpenMath. Each passage identifies how its wording was recorded.

Passage 1 · OpenMath paraphrasePermalink

notes/primes.md lines 9–15, 21–29

For every natural number n, does there exist a prime p with n < p?

Passage details

Passage ID: prime-infinitude:entry:0:v1

Source item: notes/primes.md lines 9–15, 21–29

Source record: openmath-prime-note@a640f3adfa536da0

Used in

Explicit citations in versioned problem publications. A citation records a use; it does not confer proof or independent verification.

Why are there infinitely many primes? →

Problem publication v8

The set of primes is unbounded →

Source assessment

Proved

Known theorem in authored reference note

The cited source item and version only; this is not an independent OpenMath assessment.

Observed Oct 1, 2026

There are infinitely many primes →

Source assessment

Proved

Known theorem in authored reference note

The cited source item and version only; this is not an independent OpenMath assessment.

Observed Oct 1, 2026

A prime strictly above every bound →

Source assessment

Proved

Known theorem in authored reference note

The cited source item and version only; this is not an independent OpenMath assessment.

Observed Oct 1, 2026

Problem context · 3 citations

Question

Why are there infinitely many primes?

Further reading

Read the setting and notation before comparing the results.

Credits

OpenMath staff

Versions

OpenMath source records preserve exact citations. Observation dates order these records; they do not establish the latest upstream paper or proof.

  1. a640f3adfa536da0 · selectedObserved Oct 1, 2026 · used in current publications

    OpenMath · prime note

Record details
Source ID
openmath-prime-note
Record ID
openmath-prime-note@a640f3adfa536da0
Recorded title
OpenMath · prime note
Revision
a640f3adfa536da0
Observed
Oct 1, 2026
Source updated
Sep 26, 2026
Content SHA-256
a640f3adfa536da0fb792b52610d9d9d56540fbeb430df766667a4ff65b8b49f
Update method
Manual checked import; new observations require staff preview and publication
Identifier policy
Canonical source URL plus explicit item/declaration locator; no fuzzy identity merge
Check interval
180 days
Rights
full-text
License
CC-BY-4.0

Licensed source links and exact source spans; attribution retained.

Source terms ↗