Format Euler Code

Overview

Apply the Euler C++ code-style rules so solutions are consistent, readable, and compliant. Focus on formatting, structure, and required conventions while preserving correctness.

Guidelines

• Keep helper functions and structs above main(); keep main() short and focused on orchestration and output.
• Use a single translation unit; avoid extra headers unless the problem demands it.
• List only required standard headers explicitly; avoid mega-headers.
• Qualify all standard library usage with std::; do not use using namespace std;.
• Use static_cast<...> for conversions; avoid C-style casts.
• Prefer fixed-width integers (std::uint64_t, std::int64_t) and keep constants const or constexpr near use.
• Mark file-scope helpers as static (or static inline for small helpers).
• Prefer std::vector/std::array; reserve() or pre-size when size is known; use std::size_t for indexing by size.
• Use clear loops with early-continue/early-return; avoid unnecessary recursion.
• Use std::ios::sync_with_stdio(false); std::cin.tie(nullptr); when reading input.
• End final output with std::endl.
• Keep comments short and only for non-obvious math or logic; use ASCII only; never reference AGENTS instructions.
• Use <primesieve.hpp> for prime generation when needed; use Boost multiprecision only when bounds require it.

Quick Workflow

1. Scan the file for style violations: includes, namespaces, helper placement, types, casts, and I/O setup.
2. Apply the minimal edits needed to conform to guidelines without changing logic.
3. Re-check for unnecessary headers, incorrect types, or missing static helpers.
4. Confirm the final output line ends with std::endl.
5. Confirm that the program output remains unchanged compared to prior to the code updates.