What a silly little project

.gitignore

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+# Devenv
+.devenv*
+devenv.local.nix
+devenv.local.yaml
+
+# direnv
+.direnv
+
+# pre-commit
+.pre-commit-config.yaml
+
+
+# Added by cargo
+
+/target
+.envrc

Cargo.lock

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+# This file is automatically @generated by Cargo.
+# It is not intended for manual editing.
+version = 4
+
+[[package]]
+name = "compile-time-nth-prime"
+version = "0.1.0"

Cargo.toml

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+[package]
+name = "compile-time-nth-prime"
+version = "0.1.0"
+edition = "2024"
+
+[dependencies]

devenv.lock

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+{
+  "nodes": {
+    "devenv": {
+      "locked": {
+        "dir": "src/modules",
+        "lastModified": 1777989417,
+        "narHash": "sha256-/wC0i5Wls2z66d7G8V99Vs/Mh1TZwaFotmRvY6Ygj1w=",
+        "owner": "cachix",
+        "repo": "devenv",
+        "rev": "02242113054fa55a4f1973a2d51bd996ecb8a242",
+        "type": "github"
+      },
+      "original": {
+        "dir": "src/modules",
+        "owner": "cachix",
+        "repo": "devenv",
+        "type": "github"
+      }
+    },
+    "nixpkgs": {
+      "inputs": {
+        "nixpkgs-src": "nixpkgs-src"
+      },
+      "locked": {
+        "lastModified": 1776852779,
+        "narHash": "sha256-WwO/ITisCXwyiRgtktZgv3iGhAGO+IB5Av4kKCwezR0=",
+        "owner": "cachix",
+        "repo": "devenv-nixpkgs",
+        "rev": "ec3063523dcd911aeadb50faa589f237cdab5853",
+        "type": "github"
+      },
+      "original": {
+        "owner": "cachix",
+        "ref": "rolling",
+        "repo": "devenv-nixpkgs",
+        "type": "github"
+      }
+    },
+    "nixpkgs-src": {
+      "flake": false,
+      "locked": {
+        "lastModified": 1776329215,
+        "narHash": "sha256-a8BYi3mzoJ/AcJP8UldOx8emoPRLeWqALZWu4ZvjPXw=",
+        "owner": "NixOS",
+        "repo": "nixpkgs",
+        "rev": "b86751bc4085f48661017fa226dee99fab6c651b",
+        "type": "github"
+      },
+      "original": {
+        "owner": "NixOS",
+        "ref": "nixpkgs-unstable",
+        "repo": "nixpkgs",
+        "type": "github"
+      }
+    },
+    "root": {
+      "inputs": {
+        "devenv": "devenv",
+        "nixpkgs": "nixpkgs"
+      }
+    }
+  },
+  "root": "root",
+  "version": 7
+}

devenv.nix

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+{ pkgs, ... }:
+
+{
+  # https://devenv.sh/packages/
+  packages = with pkgs; [ git ];
+
+  # https://devenv.sh/languages/
+  languages.rust.enable = true;
+
+  # See full reference at https://devenv.sh/reference/options/
+}

devenv.yaml

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+# yaml-language-server: $schema=https://devenv.sh/devenv.schema.json
+inputs:
+  nixpkgs:
+    url: github:cachix/devenv-nixpkgs/rolling
+
+# If you're using non-OSS software, you can set allowUnfree to true.
+# allowUnfree: true
+
+# If you're willing to use a package that's vulnerable
+# permittedInsecurePackages:
+#  - "openssl-1.1.1w"
+
+# If you have more than one devenv you can merge them
+#imports:
+# - ./backend

src/main.rs

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+use std::f64::consts::{LN_2, SQRT_2};
+
+const fn base_2_reduction(n: f64) -> (f64, i32) {
+    if n <= 0.0 {
+        return (n, 0);
+    }
+
+    let mut r = n;
+    let mut exp = 0i32;
+
+    while r > SQRT_2 {
+        r /= 2.0;
+        exp += 1;
+    }
+    while r < SQRT_2 / 2.0 {
+        r *= 2.0;
+        exp -= 1;
+    }
+
+    (r, exp)
+}
+
+const fn ln_taylor(z: f64) -> f64 {
+    let x1 = z - 1.0;
+    let x2 = x1 * x1;
+    let x3 = x2 * x1;
+    let x4 = x2 * x2;
+    let x5 = x3 * x2;
+    let x6 = x3 * x3;
+    let x7 = x4 * x3;
+    let x8 = x4 * x4;
+
+    x1 - x2 / 2.0 + x3 / 3.0 - x4 / 4.0 + x5 / 5.0 - x6 / 6.0 + x7 / 7.0 - x8 / 8.0
+}
+
+const fn ln(n: f64) -> f64 {
+    let (r, e) = base_2_reduction(n);
+    ln_taylor(r) + (e as f64) * LN_2
+}
+
+const fn prime_limit(n: usize) -> usize {
+    if n >= 6 {
+        let ln_n = ln(n as f64);
+        (n as f64 * (ln_n + ln(ln_n))).ceil() as usize
+    } else {
+        15
+    }
+}
+
+const fn sieve_nth_prime<const N: usize>(n: usize) -> Option<usize> {
+    if n < 1 {
+        return None;
+    }
+    if n == 1 {
+        return Some(2);
+    }
+
+    let limit = prime_limit(n);
+    let mut sieve = [true; N];
+    let mut primes = [0usize; N];
+    let mut prime_index: usize = 0;
+
+    let mut p: usize = 2;
+    while p <= limit {
+        if sieve[p] {
+            primes[prime_index] = p;
+            prime_index += 1;
+            if prime_index + 1 == n {
+                return Some(p);
+            }
+
+            let mut i = p * p;
+            while i <= limit {
+                sieve[i] = false;
+                i += p;
+            }
+        }
+
+        p += 1;
+    }
+
+    unreachable!()
+}
+
+macro_rules! nth_prime {
+    ($n:expr) => {
+        const {
+            const LIMIT: usize = prime_limit($n + 1) + 1;
+            sieve_nth_prime::<LIMIT>($n + 1).unwrap()
+        }
+    };
+}
+
+#[allow(long_running_const_eval)]
+const NTH_PRIME: usize = nth_prime!(1000000);
+
+fn main() {
+    println!("{NTH_PRIME}")
+}