From e5868c26497859adb9a2c4709f240bf73cf208a0 Mon Sep 17 00:00:00 2001
From: Sidney Zhang <zly@lyzhang.me>
Date: Tue, 3 Feb 2026 14:35:55 +0800
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---
 .../0046.GoldbachsConjecture/euler_46.py      | 81 +++++++++++++++++++
 solutions/0046.GoldbachsConjecture/readme.md  |  4 +
 2 files changed, 85 insertions(+)
 create mode 100644 solutions/0046.GoldbachsConjecture/euler_46.py
 create mode 100644 solutions/0046.GoldbachsConjecture/readme.md

diff --git a/solutions/0046.GoldbachsConjecture/euler_46.py b/solutions/0046.GoldbachsConjecture/euler_46.py
new file mode 100644
index 0000000..b898fe4
--- /dev/null
+++ b/solutions/0046.GoldbachsConjecture/euler_46.py
@@ -0,0 +1,81 @@
+"""
+It was proposed by Christian Goldbach that every odd composite number can be written as the sum of a prime and twice a square.
+
+9 = 7 + 2 * 1^2
+15 = 7 + 2 * 2^2
+21 = 3 + 2 * 3^2
+25 = 7 + 2 * 3^2
+27 = 19 + 2 * 2^2
+33 = 31 + 2 * 1^2
+
+It turns out that the conjecture was false.
+What is the smallest odd composite that cannot be written as the sum of a prime and twice a square?
+"""
+
+import math
+import time
+
+
+def timer(func):
+    def wrapper(*args, **kwargs):
+        start_time = time.time()
+        result = func(*args, **kwargs)
+        end_time = time.time()
+        print(f"{func.__name__} took {end_time - start_time:.6f} seconds")
+        return result
+
+    return wrapper
+
+
+def sieve_of_eratosthenes(limit: int = 5000) -> list[bool]:
+    """生成一个布尔数组，is_prime[i]为True表示i是质数"""
+    is_prime = [True] * (limit + 1)
+    is_prime[0:2] = [False, False]
+
+    for i in range(2, int(limit**0.5) + 1):
+        if is_prime[i]:
+            for j in range(i * i, limit + 1, i):
+                is_prime[j] = False
+    return is_prime
+
+
+def optimized_find_counterexamples(limit: int = 10000) -> list[int]:
+    """
+    优化版本，使用集合提高查找效率
+    """
+    # 生成质数表
+    is_prime = sieve_of_eratosthenes(limit)
+    primes = [i for i in range(limit + 1) if is_prime[i]]
+
+    # 预计算所有奇合数
+    odd_composites = set(n for n in range(3, limit + 1, 2) if not is_prime[n])
+
+    # 预计算2k²的值
+    max_k = int(math.sqrt(limit / 2)) + 1
+    two_k_squared = [2 * k * k for k in range(1, max_k + 1)]
+
+    # 计算所有可以表示的奇合数
+    representable_odd_composites = set()
+    for p in primes:
+        if p > limit:
+            break
+        for tks in two_k_squared:
+            n = p + tks
+            if n > limit:
+                break
+            if n in odd_composites:
+                representable_odd_composites.add(n)
+
+    # 找出不能表示的奇合数
+    return sorted(odd_composites - representable_odd_composites)
+
+
+@timer
+def main(limit: int = 20000) -> None:
+    res = optimized_find_counterexamples(limit)
+    for r in res:
+        print(r)
+
+
+if __name__ == "__main__":
+    main()
diff --git a/solutions/0046.GoldbachsConjecture/readme.md b/solutions/0046.GoldbachsConjecture/readme.md
new file mode 100644
index 0000000..6786e2c
--- /dev/null
+++ b/solutions/0046.GoldbachsConjecture/readme.md
@@ -0,0 +1,4 @@
+这个问题，怎么都不算有简洁的方式找到，暴力搜索是唯一途径，但所幸，这个搜索还算快速。
+
+另外，这个问题可以在 [OEIS](https://oeis.org/A060003) 上直接搜索到。
+这也算是最简单偷懒的方式了吧。