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In graph Frontier
MathematicsArithmeticEstablished

Prime number

A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers.

Prime numberNatural numberDivisorFundamental theorem of arithmeticRiemann hypothesisShor's algorithmLanglands programBirch–Swinnerton-Dyer conjectureInteger

At a glance

Type
patterns
Disciplines 2
MathematicsArithmetic
Mental models 0
—
Role in the graph
Cross-disciplinary bridge
reaches 2 discipline lenses

Key signals

Cross-disciplinary reach
Disciplines
2
  • Mathematics
  • Arithmetic
Evidence & development

Dependencies

What this concept builds on and what it makes possible — derived from the atlas’s dependency, causal and structural relations, not from every related edge.

Foundations · builds on

Prime numberdepends onDivisorEstablished

Open Divisor →

prime number depends on divisor.

Mechanism: A prime number is defined by its divisors: it has exactly two, one and itself, so it cannot be split into a smaller product.

Sources:

Enables · leads to

Fundamental theorem of arithmeticdepends onPrime numberEstablished

Open Fundamental theorem of arithmetic →

Primes are the building blocks of integers.

Mechanism: Every integer above one factors into primes in exactly one way, so primes generate all the integers by multiplication.

System context

Prime numberis aNatural numberEstablished

Open Natural number →

prime number is a kind of natural number.

Mechanism: A prime number is a natural number greater than 1 whose only divisors are 1 and itself.

Sources:

Structural role & consequence

Interpreted from the current atlas graph — what the connections mean, not just how many there are.

  • Removing this node severs the only sampled structural route between Birch–Swinnerton-Dyer conjecture and Shor's algorithm — a non-redundant bridge here.

    structural · Structural removal simulation — not a historical or causal counterfactual.

  • 29% of its relationships cross field boundaries, reaching 2 other disciplines — unusual in a discipline where most concepts stay within their field.

    structural · Structural graph analysis — not a claim of importance, causation or history.

  • Currently dark in the atlas: 7 of 7 of its relations lack claim-level evidence.

    atlas representation · Describes the current Thinking OS representation, not the state of the world.

  • Builds on 1 foundation (requires / depends-on / derived-from / emerges-from).

    structural · Structural graph analysis — not a claim of importance, causation or history.

29%

cross-field
5 within-field, 2 cross-field

0 of 7 relations carry evidence · concept has a verified source

Strengths & constraints

Constraints

  • Evidence coverage currently thin in the atlas — few of its relationships carry claim-level evidence. atlas representation
  • Non-redundant bridge — removing it severs a sampled route between neighbouring clusters. structural

Conditions

  • Its dependency reading rests on 1 foundation relation. structural
  • Read structurally — most of its relationships carry no external evidence yet, so claims here are graph-derived. structural

Dependency radial

What this concept builds on (left) and what it makes possible (right) — derived from dependency and causal relations.

DivisorFundamental theorem of …Prime number◀ builds onenables ▶

What builds on this

1 concept build on this directly, 1 in total, across 2 disciplines.

MathematicsNumber Theory

Structural downstream reach along dependency edges — not a claim of historical necessity.

Seen through each discipline

How this concept sits in each of its fields — derived from its real connections in the graph, not asserted.

Mathematics

Through this lens it connects to Natural number, Divisor, Fundamental theorem of arithmetic and Riemann hypothesis.

Prime number through the Mathematics lens →

Arithmetic

Through this lens it connects to Natural number and Divisor.

Prime number through the Arithmetic lens →

Formula

prime number

Source: Wikidata

Key dates

  1. c. 300 BCEFormalizationEuclid proves there are infinitely many primes in the Elements. — MacTutor History of Mathematics Archive

Check yourself

A quick check against a common misconception. Nothing is scored — picking the tempting-but-wrong answer just flags an idea worth revisiting.

Which statement is correct?

Common misconceptions

1 is a prime number.

1 has only one divisor (itself), not two, so it is not prime. Excluding it keeps prime factorisation unique.

Look for: Learner lists 1 among the primes.

Concepts that look related but are not yet connected here — candidates for a connection to reason about, not established links.

This idea also appears in…

The same structure shows up in other disciplines. These are real recurrences drawn from the graph — a starting point for asking “what carries over, and what changes?”

Concepts

Explained by stage
lower secondary

A prime number is a whole number bigger than 1 that can only be divided evenly by 1 and itself — like 2, 3, 5, 7, 11. Every other whole number can be built by multiplying primes together.

upper secondary

A prime has exactly two distinct divisors, 1 and itself. Primes are the multiplicative building blocks of the integers: the fundamental theorem of arithmetic says every integer above 1 factors into primes in exactly one way.

The scientific picture
  • Connects 7 other ideas across 2 disciplines.
  • A cross-disciplinary bridge — its connections reach into 2 other fields.
  • Most of its connections are of the “Teaching link” kind.

Derived from the graph’s real structure — observations, not a score.

Sources