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  "body": "\n## Statement\n\nLet $p$ be a [[prime number|0SN0MAEKYX]].\nThen $\\varphi(p) = p - 1$, where $\\varphi$ is [[Euler's totient function|0VV04M41AN]].\n\n## Remarks\n\nThe proof: the only divisors of $p$ are $1$ and $p$. So each of $1, \\dots, p - 1$ is coprime to $p$, and $p$ is not.\nThe converse holds: if $n \u003e 1$ and $\\varphi(n) = n - 1$, then $n$ is prime.\nThe result is the case $k = 1$ of the [[totient of a prime power|0AVY8HKBGD]].\n\n## Explanations\n\n### L1 human\n\nFor a prime $p$, each number from $1$ to $p - 1$ has no common factor with $p$.\nFor example, $\\varphi(7) = 6$, because $1, 2, 3, 4, 5, 6$ are all coprime to $7$.\n",
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