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  "body": "\n## Statement\n\nThere are infinitely many [[prime numbers|0SN0MAEKYX]] $p$ such that $p + 2$ is also prime.\n\n## Remarks\n\nA pair of primes $(p, p + 2)$ is a pair of twin primes. The first pairs are $(3, 5)$, $(5, 7)$, $(11, 13)$, $(17, 19)$, $(29, 31)$.\nThe conjecture is the case $k = 1$ of the conjecture of de Polignac: for each positive integer $k$, there are infinitely many primes $p$ such that $p + 2k$ is prime.\nThe conjecture is open.\n\n## History\n\nDe Polignac stated the general conjecture in 1849.\nIn 2013, Yitang Zhang proved that some gap $N \u003c 7 \\cdot 10^7$ occurs between infinitely many pairs of primes. Later work by Maynard and the Polymath project reduced the bound to $246$.\n\n## Explanations\n\n### L1 human\n\nTwin primes are primes with only one number between them, like $41$ and $43$.\nThe conjecture says that such pairs never stop, even though primes become rarer.\n",
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