Eratosthenes spiral
E404062
The Eratosthenes spiral is a geometric visualization of prime numbers generated by the sieve of Eratosthenes, arranging integers in a spiral so that primes form distinctive radial patterns.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Eratosthenes spiral canonical | 1 |
| Sieve of Eratosthenes | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T3987367 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Eratosthenes spiral Context triple: [Ulam spiral, relatedConcept, Eratosthenes spiral]
-
A.
Ulam spiral
The Ulam spiral is a graphical arrangement of the positive integers in a spiral pattern that reveals striking diagonal alignments of prime numbers, suggesting unexpected structure in their distribution.
-
B.
Archimedes' spiral
Archimedes' spiral is a classical mathematical curve that winds outward from a fixed point at a constant rate as it revolves around that point.
-
C.
On Spirals
On Spirals is a mathematical treatise by Archimedes in which he systematically studies the properties and applications of spiral curves, especially the Archimedean spiral.
-
D.
Lyapunov fractal
The Lyapunov fractal is a complex, self-similar pattern arising from iterating logistic maps with periodically varying parameters, used to visualize stability and chaos in dynamical systems.
-
E.
Ulam sequence
The Ulam sequence is an integer sequence starting with 1 and 2 in which each subsequent term is the smallest integer that can be written uniquely as the sum of two distinct earlier terms.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Eratosthenes spiral Target entity description: The Eratosthenes spiral is a geometric visualization of prime numbers generated by the sieve of Eratosthenes, arranging integers in a spiral so that primes form distinctive radial patterns.
-
A.
Ulam spiral
The Ulam spiral is a graphical arrangement of the positive integers in a spiral pattern that reveals striking diagonal alignments of prime numbers, suggesting unexpected structure in their distribution.
-
B.
Archimedes' spiral
Archimedes' spiral is a classical mathematical curve that winds outward from a fixed point at a constant rate as it revolves around that point.
-
C.
On Spirals
On Spirals is a mathematical treatise by Archimedes in which he systematically studies the properties and applications of spiral curves, especially the Archimedean spiral.
-
D.
Lyapunov fractal
The Lyapunov fractal is a complex, self-similar pattern arising from iterating logistic maps with periodically varying parameters, used to visualize stability and chaos in dynamical systems.
-
E.
Ulam sequence
The Ulam sequence is an integer sequence starting with 1 and 2 in which each subsequent term is the smallest integer that can be written uniquely as the sum of two distinct earlier terms.
- F. None of above. chosen
Statements (43)
| Predicate | Object |
|---|---|
| instanceOf |
geometric construction
ⓘ
mathematical visualization ⓘ |
| aimsToHighlight | structure in prime distribution beyond simple plots ⓘ |
| arranges | positive integers ⓘ |
| basedOn | sieve of Eratosthenes ⓘ |
| canBeAnalyzedUsing |
computational experiments
ⓘ
visual pattern recognition ⓘ |
| canBeExtendedTo | large ranges of integers ⓘ |
| canBeRenderedAs |
computer-generated image
ⓘ
hand-drawn diagram ⓘ |
| category |
mathematical art
ⓘ
prime number visualization ⓘ |
| constructionStep |
apply sieve of Eratosthenes to mark primes
ⓘ
highlight or color prime positions ⓘ place integers sequentially along a spiral curve ⓘ |
| contrastWith |
randomized prime visualizations
ⓘ
rectangular lattice prime plots ⓘ |
| coordinateSystem | polar coordinates ⓘ |
| dependsOn |
classification of numbers as prime or composite
ⓘ
ordering of natural numbers ⓘ |
| displays | radial patterns of primes ⓘ |
| emphasizes | geometric aspects of prime distribution ⓘ |
| field |
discrete mathematics
ⓘ
mathematical visualization ⓘ number theory ⓘ |
| hasInput | sequence of natural numbers ⓘ |
| hasLayout | spiral ⓘ |
| hasOutput | spiral diagram with primes emphasized ⓘ |
| hasProperty |
composite numbers form complementary patterns
ⓘ
primes tend to align along rays ⓘ |
| hasVisualFeature |
curved bands of composite numbers
ⓘ
radial lines with high density of primes ⓘ |
| inspiredBy |
sieve of Eratosthenes
ⓘ
surface form:
classical sieve of Eratosthenes
|
| isAlternativeTo | Ulam spiral for visualizing primes ⓘ |
| namedAfter |
Eratosthenes
ⓘ
surface form:
Eratosthenes of Cyrene
|
| purpose | to reveal visual structure in the distribution of prime numbers ⓘ |
| relatedTo |
Ulam spiral
ⓘ
Ulam spiral ⓘ
surface form:
prime number spiral
|
| shows | non-random visual patterns of primes ⓘ |
| usedIn |
educational demonstrations of prime distribution
ⓘ
visual exploration of number-theoretic patterns ⓘ |
| usesMethod | iterative elimination of composite numbers ⓘ |
| visualizes | prime numbers ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Eratosthenes spiral Description of subject: The Eratosthenes spiral is a geometric visualization of prime numbers generated by the sieve of Eratosthenes, arranging integers in a spiral so that primes form distinctive radial patterns.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Sieve of Eratosthenes