Question

# Primality Testing with the Rabin-Miller Algorithm

import random


def rabinMiller(num):
    # Returns True if num is a prime number.

    s = num - 1
    t = 0
    while s % 2 == 0:
        # keep halving s while it is even (and use t
        # to count how many times we halve s)
        s = s // 2
        t += 1

    for trials in range(5): # try to falsify num's primality 5 times
        a = random.randrange(2, num - 1)
        v = pow(a, s, num)
        if v != 1: # this test does not apply if v is 1.
            i = 0
            while v != (num - 1):
                if i == t - 1:
                    return False
                else:
                    i = i + 1
                    v = (v ** 2) % num
    return True


def isPrime(num):
    # Return True if num is a prime number. This function does a quicker
    # prime number check before calling rabinMiller().

    if (num < 2):
        return False # 0, 1, and negative numbers are not prime

    # About 1/3 of the time we can quickly determine if num is not prime
    # by dividing by the first few dozen prime numbers. This is quicker
    # than rabinMiller(), but unlike rabinMiller() is not guaranteed to
    # prove that a number is prime.

    lowPrimes = [[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53,
59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139,
149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229,
233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317,
331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421,
431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521,
523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619,
631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733,
739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839,
853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953,
967, 971, 977, 983, 991, 997]]

    if num in lowPrimes:
        return True

    # See if any of the low prime numbers can divide num
    for prime in lowPrimes:
        if (num % prime == 0):

            return False

    # If all else fails, call rabinMiller() to determine if num is a prime.
    return rabinMiller(num)


def generateLargePrime(keysize=1024):
    # Returns a random prime number of keysize bits in size.
    while True:
        num = random.randrange(2**(keysize-1), 2**(keysize))
        if isPrime(num):
            return num

我正在创建一个Python程序，它会告诉你数字是否为素数。它基本上是拉宾米勒算法，但在第60行，我的程序停止，我得到错误：

TypeError: unsupported operand type(s) for %: 'int' and 'list'.

这是第60行： lowPrimes = [[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, ...]]

我做错了什么？

Answer 1

您的lowPrimes变量是一个列表列表，因此当您说for prime in lowPrimes时，prime是一个列表，因此您无法通过int来模拟list一个lowPrimes = [[...]]。尝试将lowPrimes = [...]更改为%（删除一层括号）。

错误信息在这里很有启发性。它表示您正在尝试将int运算符应用于list和prime。由于您还有行号，您可以看到它所引用的表达式，{{1}}必须是一个列表。

Answer 2

您的lowPrimes数组的定义方式错误。您希望它是一个数字列表，而是一个数字列表列表（外部列表只包含一个元素）。这会导致您在迭代lowPrimes的所有元素时看到的错误，并检查您的号码是否可以被lowPrimes的元素分割。要解决此问题，请删除外部方括号：

lowPrimes = [[2, 3, 5, 7, 11, 13, 17, 19, ... 997]]

=＆GT;

lowPrimes = [2, 3, 5, 7, 11, 13, 17, 19, ... 997]

TypeError对于不支持的操作数类型＆＃39; int＆＃39;和＆＃39;列出＆＃39;

2 个答案: