# A report onTwin prime, Prime number and Yitang Zhang         A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair (41, 43).

- Twin prime

The breakthrough work of Yitang Zhang in 2013, as well as work by James Maynard, Terence Tao and others, has made substantial progress towards proving that there are infinitely many twin primes, but at present this remains unsolved.

- Twin prime

These include Goldbach's conjecture, that every even integer greater than 2 can be expressed as the sum of two primes, and the twin prime conjecture, that there are infinitely many pairs of primes having just one even number between them.

- Prime number

On April 17, 2013, Zhang announced a proof that states there are infinitely many pairs of prime numbers that differ by 70 million or less.

- Yitang Zhang

This result implies the existence of an infinitely repeatable prime 2-tuple, thus establishing a theorem akin to the twin prime conjecture.

- Yitang Zhang

The mathematical theory of prime numbers also moved forward with the Green–Tao theorem (2004) that there are arbitrarily long arithmetic progressions of prime numbers, and Yitang Zhang's 2013 proof that there exist infinitely many prime gaps of bounded size.

- Prime number 