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  "body": "\n## Definition\n\nFor a real number $x$, the prime-counting function $\\pi(x)$ is the number of [[prime numbers|0SN0MAEKYX]] $p$ with $p \\le x$.\n\n## Remarks\n\nFor example, $\\pi(10) = 4$, because the primes up to $10$ are $2, 3, 5, 7$. Also $\\pi(100) = 25$.\nThe function is a step function. It increases by $1$ at each prime.\nThe [[prime number theorem|0EHBY5Y84N]] says that $\\pi(x)$ grows like $x / \\ln x$.\nThe symbol $\\pi$ here has no relation to the number $3.14159\\dots$.\n\n## Explanations\n\n### L1 human\n\nThe function $\\pi(x)$ answers the question: how many primes are there up to $x$?\nThe answer grows without bound, by [[Euclid's theorem|0292EPPPT0]], but the primes become rarer as $x$ grows.\n",
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