Linked from

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

• 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.

• 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.

• 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.

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

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

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

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

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

• 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.

• 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.

• 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.

• 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.

• Fermat numberRelated: Whether a Fermat number is prime is the sequence’s central arithmetic question.

• Catalan's conjectureRelated: The theorem's exceptional powers, 2³ and 3², have prime bases.

• Hensel's lemmaRelated: The theorem organizes its approximations by powers of a chosen prime.

• Divisibility ruleRelated: Testing prime divisors can establish whether a number is prime.

• Erdős–Straus conjectureRelated: Prime inputs form a central subproblem in attempts to prove the conjecture.

• Aliquot sequenceRelated: A prime has proper-divisor sum 1, so its sequence proceeds to 1 and then 0.

• Freshman's dreamRelated: The identity's exponent is prime, which ensures all intermediate binomial coefficients are divisible by p.

• Highly composite numberRelated: Only small primes appear in the factorization of a highly composite number.

• Lifting-the-exponent lemmaRelated: The lemma concerns valuations at a prime, with different conditions for odd primes and 2.

• Sophie Germain's identityRelated: The factorization gives divisibility tools in problems about primes and fourth powers.

• Aliquot sumRelated: Every prime has aliquot sum one because its only proper divisor is one.

• Midy's theoremRelated: The denominator p is prime, which structures the modular remainders behind the result.

• Von Staudt–Clausen theoremRelated: Only primes satisfying p−1 dividing 2n occur in the stated denominator.