Twin prime conjecture

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The twin prime conjecture concerns twin primes, which are primes $p$ such that $p+2$ is also prime.

Conjecture (Twin prime conjecture).

There are infinitely many twin primes.

It has long been known that there are infinitely many primes, but whether the same is true of the twin primes is one of the longest-standing conjectures in number theory.

As of 2011, the largest known twin prime pair is 3756801695685 × 2⁶⁶⁶⁶⁶⁹ ± 1.

See also

• Strong twin prime conjecture
• K-tuple conjecture
• Euclid's proof that there are infinitely many primes