86 lines
2.5 KiB
Python
86 lines
2.5 KiB
Python
"""
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The arithmetic sequence, 1487,4817,8147, in which each of the terms increases by 3330,
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is unusual in two ways: (i) each of the three terms are prime, and, (ii) each of the
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4-digit numbers are permutations of one another.
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There are no arithmetic sequences made up of three 1-, 2-, or 3-digit primes, exhibiting this property,
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but there is one other 4-digit increasing sequence.
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What 12-digit number do you form by concatenating the three terms in this sequence?
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"""
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import time
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def timer(func):
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def wrapper(*args, **kwargs):
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start_time = time.time()
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result = func(*args, **kwargs)
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end_time = time.time()
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elapsed_time = end_time - start_time
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print(f"{func.__name__} time: {elapsed_time:.6f} seconds")
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return result
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return wrapper
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def list_primes(start: int, end: int) -> list[int]:
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# 只需要筛到 sqrt(9999) ≈ 100 即可标记合数
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limit = int(end**0.5) + 1
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base_primes = [True] * limit
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base_primes[0] = base_primes[1] = False
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# 生成基础质数（2到100）
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for i in range(2, int(limit**0.5) + 1):
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if base_primes[i]:
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for j in range(i * i, limit, i):
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base_primes[j] = False
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# 分段筛：只标记1000-9999范围
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size = end - start + 1
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is_prime = [True] * size
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for p in range(2, limit):
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if base_primes[p]:
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# 找到第一个大于等于start的p的倍数
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first = max(p * p, ((start + p - 1) // p) * p)
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for j in range(first, end + 1, p):
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is_prime[j - start] = False
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return [i + start for i, val in enumerate(is_prime) if val]
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def list_com(a: list, b: list) -> bool:
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if len(set(a)) != len(set(b)):
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return False
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xb = b.copy()
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for x in a:
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if x not in xb:
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return False
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else:
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xb.remove(x)
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return True
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@timer
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def main():
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primes = list_primes(1000, 9999)
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max_sp = max(primes)
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res = []
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for i, v in enumerate(primes):
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if v == max_sp:
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break
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gap = int((max_sp - v) / 3)
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for g in range(gap, (primes[i + 1] - v - 1), -1):
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if v + g in primes and v + 2 * g in primes:
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if list_com(list(str(v)), list(str(v + g))):
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if list_com(list(str(v)), list(str(v + 2 * g))):
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res.append(str(v) + str(v + g) + str(v + 2 * g))
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else:
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continue
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print(res)
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if __name__ == "__main__":
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main()
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