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

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

• 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.

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

• 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.

• 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.

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

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

• 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.

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

• 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.

• Fermat's theorem on sums of two squaresNarrower topic: The theorem classifies which odd primes admit the specified square representation.

• Legendre's conjectureNarrower topic: The conjecture asks whether every interval between consecutive squares contains one.

• Sophie Germain primeNarrower topic: The defining condition requires p itself to be prime.

• Twin primeNarrower topic: Each member of a twin-prime pair must be prime.

• Vinogradov's theoremNarrower topic: These are the summands whose additive representations the theorem guarantees.

• Wilson's theoremNarrower topic: Primality is exactly the property characterized by Wilson's factorial congruence.

• Euclid–Euler theoremNarrower topic: Primality of 2^p−1 is the theorem's condition on the exponent-dependent factor.

• Legendre's formulaNarrower topic: The formula takes a prime as its input and counts its power in a factorial.

• Sum of two squares theoremNarrower topic: The theorem’s test is stated separately for each prime divisor.

• Bunyakovsky conjectureNarrower topic: The conjecture predicts infinitely many outputs that meet this definition.

• Bonse's inequalityNarrower topic: Every factor in the inequality's product, and the next term, is prime.

• Sophie Germain's theoremNarrower topic: Both p and 2p+1 must be prime for the theorem’s stated conclusion.

• Agoh–Giuga conjectureNarrower topic: The conjecture proposes a congruence that characterizes exactly these integers.

• Beal's conjectureNarrower topic: The conclusion concerns a prime dividing all three bases.

• Brocard's conjectureNarrower topic: The conjecture counts primes inside each interval.

• Catalan–Mersenne conjectureNarrower topic: The conjecture concerns how often primality occurs along the recursively defined sequence.

• Friedlander–Iwaniec theoremNarrower topic: The theorem asserts primality for infinitely many values of its polynomial expression.

• Goldbach–Euler theoremNarrower topic: These are the permitted summands in the conjecture.

• Grimm's conjectureNarrower topic: Only primes may serve as the distinct divisors in the conjecture.

• Lemoine's conjectureNarrower topic: The conjecture's two summands are required to be prime.

• Ostrowski's theoremNarrower topic: Each non-Archimedean class in the theorem is indexed by a prime.

• Schinzel's theoremNarrower topic: The theorem counts distinct prime moduli, rather than roots over one fixed field.

• Wolstenholme's theoremNarrower topic: The modulus and the theorem's condition are both governed by a prime p.