Twin Prime Conjecture

The Twin Prime Conjecture is a famous unsolved problem in number theory. It proposes:

There are infinitely many twin primes.

Twin primes are pairs of prime numbers that differ by 2. Examples include:

(3, 5)
(5, 7)
(11, 13)
(17, 19)
(29, 31)
…

Formally, a pair $(p, p + 2)$ is a twin prime pair if both $p$ and $p + 2$ are prime.

First formulated by ancient Greek mathematicians but formally conjectured in modern terms in the 19th century.
It remains unproven whether there are infinitely many such pairs.

In 2013, Yitang Zhang made a breakthrough by proving that there are infinitely many pairs of primes less than 70 million apart.
Since then, this “bounded gaps between primes” result has been improved drastically by the Polymath Project, lowering the bound to 246 (as of 2014).
But this is still not 2, so the Twin Prime Conjecture remains unresolved.

Prime Gaps: Differences between consecutive primes.
Hardy–Littlewood Conjecture: Offers a general prediction about the distribution of twin primes.
Sieve of Eratosthenes and Sieve methods: Used to search for primes and understand their patterns.

Would you like a visual explanation, code to search for twin primes, or a deeper dive into Yitang Zhang’s proof?

ByteCrypt