# Twin prime conjecture

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## Statement

There are infinitely many twin primes. In other words, there are infinitely many odd primes  such that  is also a prime.

In other words, the limit inferior of all prime gaps is .

## Relation with other conjectures and known facts

### Limit inferior of prime gaps

The twin primes conjecture can be viewed as saying that the lim inf of prime gaps is . For more results on the current state of the art in knowing of the limit inferior of prime gaps (both unconditional and conditional to various hypotheses) see the prime gap page.