twin prime conjecture
E451529
The twin prime conjecture is an unsolved problem in number theory asserting that there are infinitely many pairs of prime numbers that differ by 2.
Statements (44)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical conjecture
ⓘ
unsolved problem in number theory ⓘ |
| consequenceIfTrue |
infinitely many primes p such that p and p+2 are both prime
ⓘ
there are infinitely many prime gaps equal to 2 ⓘ |
| difficulty | unsolved for more than a century ⓘ |
| doesNotClaim |
density of twin primes
ⓘ
formula for twin primes ⓘ |
| field | number theory ⓘ |
| historicalAttribution |
often attributed to Alphonse de Polignac
ⓘ
studied by Atle Selberg NERFINISHED ⓘ studied by G. H. Hardy NERFINISHED ⓘ studied by J. E. Littlewood NERFINISHED ⓘ studied by James Maynard ⓘ studied by Paul Erdős ⓘ studied by Terence Tao NERFINISHED ⓘ studied by Viggo Brun NERFINISHED ⓘ studied by Yitang Zhang ⓘ |
| implies | existence of infinitely many twin prime pairs (p,p+2) ⓘ |
| involvesConcept |
infinite set
ⓘ
prime gaps ⓘ prime number ⓘ twin primes ⓘ |
| knownEvidence |
heuristic support from Hardy–Littlewood k-tuple conjecture
ⓘ
numerical verification for very large ranges of integers ⓘ probabilistic models of primes suggest infinitude of twin primes ⓘ |
| openQuestion |
exact distribution of twin primes
ⓘ
whether there are infinitely many twin primes ⓘ |
| relatedConcept |
Brun sieve
ⓘ
Brun's constant NERFINISHED ⓘ |
| relatedConjecture |
Goldbach conjecture
NERFINISHED
ⓘ
Hardy–Littlewood prime k-tuple conjecture NERFINISHED ⓘ Polignac's conjecture NERFINISHED ⓘ prime k-tuple conjecture NERFINISHED ⓘ |
| relatedResult |
Brun proved convergence of the sum of reciprocals of twin primes
NERFINISHED
ⓘ
Hardy–Littlewood conjectured an asymptotic formula for twin primes ⓘ Maynard–Tao method improved bounds on prime gaps ⓘ Zhang proved bounded gaps between primes ⓘ bounded gaps between primes theorem ⓘ |
| relatedSequence | sequence of twin primes (3,5),(5,7),(11,13),(17,19),... ⓘ |
| specialCaseOf | Polignac's conjecture NERFINISHED ⓘ |
| statement | there exist infinitely many pairs of prime numbers that differ by 2 ⓘ |
| status | open ⓘ |
| subfield |
analytic number theory
ⓘ
prime number theory ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.