The twin prime conjecture
Twin primes are pairs of primes that differ by 2, such as or . Prove that there are infinitely many twin prime pairs.
History and references
Still open as of 2026.
The question is old enough that its origin is unclear. In 1849 Alphonse de Polignac conjectured more generally that every even number occurs infinitely often as the gap between consecutive primes, and the case of gap 2 is the twin prime conjecture. For a long time nobody could prove that any fixed gap occurs infinitely often. In 2013 Yitang Zhang proved that some gap below 70 million does. James Maynard and Terence Tao then found a simpler method, and together with the Polymath project the bound came down to 246 within a year. Closing the distance from 246 to 2 is still out of reach.
References
Solutions 0
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