✨ feat(main.py)：重构主函数调用方式，将 app() 调用封装到 main() 函数中

✨ feat(euler_37.py)：添加截断质数问题的初始实现
✨ feat(euler_37_primeclass.py)：添加基于质数生成器的截断质数完整解决方案
📝 docs(millerrabin_test.pdf)：添加 Miller-Rabin 测试的详细文档

solutions/0037.TruncatablePrimes/euler_37_primeclass.py

@@ -0,0 +1,171 @@
+"""
+The number 3797 has an interesting property.
+Being prime itself, it is possible to continuously remove digits from left to right,
+and remain prime at each stage: 3797, 797, 97, and 7.
+Similarly we can work from right to left: 3797, 379, 37, and 3.
+
+Find the sum of the only eleven primes that are both truncatable from left to right and right to left.
+
+NOTE: 2, 3, 5, and 7 are not considered to be truncatable primes.
+"""
+
+import math
+import random
+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__} taken: {end_time - start_time:.6f} seconds")
+        return result
+
+    return wrapper
+
+
+def miller_rabin_test(n: int, k: int = 10) -> bool:
+    if n < 2:
+        return False
+    if n == 2 or n == 3:
+        return True
+    if n % 2 == 0 or n % 3 == 0:
+        return False
+    r, s = 0, n - 1
+    while s % 2 == 0:
+        r += 1
+        s //= 2
+    for _ in range(k):
+        a = random.randrange(2, n - 1)
+        x = pow(a, s, n)
+        if x == 1 or x == n - 1:
+            continue
+        for _ in range(r - 1):
+            x = pow(x, 2, n)
+            if x == n - 1:
+                break
+        else:
+            return False
+    return True
+
+
+class PrimeGenerator:
+    """质数生成器"""
+
+    _cache = []
+
+    def __init__(self):
+        # self._cache = []  # 缓存已生成的质数
+        self._generator = self._prime_generator()
+
+    @classmethod
+    def is_prime(cls, n: int) -> bool:
+        """检查是否为质数（使用缓存优化）"""
+        if n < 2:
+            return False
+
+        # 检查缓存
+        if cls._cache:
+            limit = int(math.isqrt(n))
+            for p in cls._cache:
+                if p > limit:
+                    break
+                if n % p == 0:
+                    return False
+
+        # 使用Miller-Rabin测试
+        return miller_rabin_test(n)
+
+    def _prime_generator(self):
+        """生成质数的内部生成器"""
+        n = 2
+        yield n
+
+        n = 3
+        while True:
+            if self.is_prime(n):
+                PrimeGenerator._cache.append(n)
+                yield n
+            n += 2
+
+    def __iter__(self):
+        return self
+
+    def __next__(self) -> int:
+        return next(self._generator)
+
+    def __call__(self, start: int = 2):
+        """从指定位置开始生成质数"""
+        # 重置生成器到指定位置
+        self._generator = self._prime_generator_from(start)
+        return self
+
+    def _prime_generator_from(self, start: int):
+        """从指定位置开始的生成器"""
+        if start < 2:
+            n = 2
+        else:
+            n = start if start % 2 else start + 1
+
+        while True:
+            if self.is_prime(n):
+                yield n
+            n += 2
+
+    def primes_up_to(self, limit: int):
+        """生成所有不超过limit的质数"""
+        if limit < 2:
+            return
+
+        yield 2
+
+        n = 3
+        while n <= limit:
+            if self.is_prime(n):
+                yield n
+            n += 2
+
+    def nth_prime(self, n: int) -> int:
+        """获取第n个质数（从1开始）"""
+        if n < 1:
+            raise ValueError("n必须大于0")
+
+        # 如果已经在缓存中，直接返回
+        if n <= len(PrimeGenerator._cache):
+            return PrimeGenerator._cache[n - 1]
+
+        # 否则继续生成直到第n个
+        gen = self._prime_generator()
+        for _ in range(n):
+            result = next(gen)
+        return result
+
+
+def truncate_number(number: int) -> list[int]:
+    """生成一个数的所有截断形式"""
+    str_num = str(number)
+    return [int(str_num[:i]) for i in range(1, len(str_num))] + [
+        int(str_num[i:]) for i in range(len(str_num))
+    ]
+
+
+@timer
+def main() -> None:
+    primes = PrimeGenerator()
+    res = []
+    n = 0
+    while n < 11:
+        prime = next(primes)
+        if prime < 10:
+            continue
+        truncate = truncate_number(prime)
+        if all(primes.is_prime(trunc) for trunc in truncate):
+            res.append(prime)
+            print(prime)
+            n += 1
+    print(f"Sum is : {sum(res)}")
+
+
+if __name__ == "__main__":
+    main()