KnowraTwin prime conjectureLinked fromLinked fromThe 15 pages that link to Twin prime conjecture, each with the reason it gives.All 15Broader topic 3Related 5Compared with 7Number theoryBroader topic: It asks whether primes continue to occur at a fixed small gap, despite their irregular distribution.Prime number theoremCompared with: The theorem counts primes overall but does not settle whether close pairs persist indefinitely.Dirichlet's theorem on arithmetic progressionsCompared with: Dirichlet handles one fixed residue class, not the simultaneous primality constraints in prime pairs.Prime gapsRelated: It asks whether the smallest possible gap greater than zero occurs infinitely often.Sieve theoryRelated: Sieve methods give strong bounds on twin-prime counts but cannot isolate prime pairs alone.Analytic number theoryRelated: It remains beyond current sieve results, despite proofs of bounded gaps between primes.Goldbach's conjectureCompared with: It is another famous unresolved statement about the distribution of prime numbers.Additive number theoryRelated: It concerns prime patterns rather than representations, but shares sieve and distribution obstacles.Bombieri–Vinogradov theoremCompared with: The theorem supports bounded-gap progress but does not prove the twin-prime conjecture.Green–Tao theoremCompared with: It asks for a fixed gap, a feature not supplied by arbitrarily long progressions with varying gaps.Hardy–Littlewood conjecturesBroader topic: It is the prime-pair case for gap two, with a predicted asymptotic count.Twin primeBroader topic: It asks whether twin-prime pairs continue without bound.Brun's theoremCompared with: Brun's theorem leaves this central existence question unanswered.Bunyakovsky conjectureCompared with: It is another unproved prediction about prime patterns, corresponding to simultaneous linear polynomial values.Goldbach–Euler theoremRelated: It is another famous unproved claim about how primes are distributed.