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The 88 pages that link to Prime number, each with the reason it gives.

• IntegerBroader topic: Primes are the indivisible building blocks of positive integers greater than one.

• DivisibilityRelated: Prime divisors are the irreducible building blocks of positive integers.

• Euclid's ElementsRelated: Book IX proves that prime numbers are infinite in number.

• Finite fieldRelated: Every finite field has characteristic equal to a prime.

• Natural numberBroader topic: Primes are the multiplicative building blocks of natural numbers greater than one.

• Number theoryBroader topic: Primes are the indivisible building blocks underlying integer factorization.

• EuclidRelated: The Elements includes Euclid’s proof that there are infinitely many primes.

• Diophantine equationRelated: Prime factorization helps analyze powers and factorization constraints in integer solutions.

• Prime factorizationNarrower topic: Prime numbers are the indivisible factors used in the decomposition.

• Greatest common divisorRelated: Prime divisors expose the shared building blocks of integer inputs.

• Fermat's Last TheoremRelated: The exponent can be reduced to prime exponents, together with the special fourth-power case.

• Prime-counting functionNarrower topic: These are precisely the numbers counted by π(x).

• Fundamental theorem of arithmeticNarrower topic: The theorem identifies primes as the indivisible factors from which every integer above 1 is built.

• Fermat's little theoremNarrower topic: Primality ensures every nonzero residue modulo p has a multiplicative inverse.

• Integer factorizationNarrower topic: Prime numbers are the indivisible factors that form every integer's canonical decomposition.

• Congruence (number theory)Related: Prime moduli make every nonzero residue invertible.

• Coprime integersNarrower topic: Shared prime divisors reveal when two integers are not coprime.

• Euler's totient functionBroader topic: For prime p, every smaller positive integer is coprime to p, so φ(p) = p − 1.

• Pierre de FermatRelated: Fermat investigated prime numbers and proposed a theorem about primes dividing numbers of a special form.

• Dirichlet's theorem on arithmetic progressionsNarrower topic: The theorem asserts infinitely many terms of this kind.

• Prime gapsNarrower topic: Prime gaps describe the spacing within this sequence of numbers.

• Quadratic reciprocityRelated: The reciprocity law’s basic statement concerns pairs of distinct odd primes.

• Sieve theoryNarrower topic: Primes are the divisors whose multiples the sieve removes.

• Twin prime conjectureNarrower topic: Twin primes are pairs drawn from the prime numbers.

• Dirichlet seriesRelated: Prime factorization explains Euler products for series with multiplicative coefficients.

• Composite numberCompared with: Unlike a composite number, a prime has no factorization into smaller positive integers.

• Goldbach's conjectureNarrower topic: The conjecture asks whether every eligible even number can be built from two primes.

• Disquisitiones ArithmeticaeRelated: The book develops results about primes, including criteria for testing whether numbers divide one another.

• Euclid's lemmaNarrower topic: The lemma's special force comes from the defining divisibility properties of primes.

• Legendre symbolRelated: The denominator must be an odd prime for the Legendre symbol's standard definition.

• Multiplicative functionRelated: Prime factors are the atoms used to assemble every positive integer.

• Trial divisionRelated: Testing prime candidates is sufficient because every composite number has a prime factor.

• Divisor functionRelated: Prime powers are the factors on which divisor-function formulas are first evaluated.

• Mersenne primeNarrower topic: Mersenne primes are a structured, highly searchable family within the primes.

• Sieve of EratosthenesNarrower topic: The sieve preserves precisely these numbers while crossing out their composite multiples.

• Frobenius endomorphismRelated: The exponent p is the prime characteristic of the field.

• Lagrange's four-square theoremRelated: Representing primes suffices once the four-square identity handles products.

• OneCompared with: One is excluded from the primes despite having only one positive divisor.

• Euler's criterionNarrower topic: Primality makes the nonzero residue classes a field and enables the criterion.

• Rational root theoremRelated: Prime factorization underlies the theorem’s divisibility argument.

• Set-builder notationRelated: The primes can be specified as natural numbers satisfying a divisibility condition.

• Least common multipleBroader topic: Prime factors provide the indivisible building blocks used to compute the result.

• Minimal elementBroader topic: Each prime is minimal among integers greater than one ordered by divisibility.

• Even numberCompared with: Every even integer greater than 2 is composite, leaving 2 as the sole even prime.

• Green–Tao theoremBroader topic: These are the terms from which the theorem's progressions are formed.

• Perfect numberRelated: Prime factorization makes the divisor sums of perfect numbers calculable.

• Peter Gustav Lejeune DirichletRelated: The distribution of primes is the central subject of his famous progression theorem.

• Arithmetic functionRelated: Prime inputs often determine an arithmetic function’s behavior on all integers.

• Édouard LucasNarrower topic: Primality testing was a central theme in Lucas’s number-theoretic work.

• Euclid's theoremNarrower topic: The theorem concerns the size of this set of numbers.