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

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

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

• 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.

• 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.

• Number (mathematics)Broader topic: Primes are the multiplicative building blocks of the positive integers.

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

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

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

• 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.

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

• 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.

• 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.

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

• 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.

• Mathematical conceptsBroader topic: Primes are elementary objects with deep roles in number theory and cryptography.

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

• 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.

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

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