用Python寻找质数

本文中所用的的方法在一个pdf中，我会在文末将其上传

第一种方法寻找指数

import math
def isPrime(num):
    
    if num < 2:
        print("该数不是素数")
    # see if num is divisible by any number up to the square root of num
    else:
        for i in range (2, int(math . sqrt(num) ) +1):
            if num % i == 0:
                print("该数不是素数")
            else:
                print("该数是素数")
num = int(input("请输入第一个数: "))
isPrime(num)

第二种方法寻找指数

import math
# all numbers less than 2 are not prime
def primeSieve(sieveSize) :
    # Returns a list of prime numbers calculated using
    # the Sieve of Eratosthenes algorithm .
    sieve = [True] * sieveSize
    sieve[0] = False # zero and one are not prime numbers
    sieve[1] = False
    # create the sieve
    for i in range(2, int(math . sqrt (sieveSize )) +1):
        pointer = i * 2
        while pointer < sieveSize:
            sieve[pointer] = False
            pointer += i
    # compile the list of primes
    # compile the list of prime
    primes = []
    for i in range(sieveSize) :
        if sieve[i] == True :
            primes.append(i)
    print(primes)
sieveSize = int(input("请用第二种方法计算： "))
primeSieve(sieveSize)

判断是否是质数的方法

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):
    if (num < 2):
        return False # 0, 1, and negative numbers are not prime
    lowPrimes = [1,2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,
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):
# Return a random prime number of keysize bits in size .
    while True:
        num = random.randrange (2** (keysize - 1), 2** (keysize) )
        if isPrime(num):
            return num

https://download.csdn.net/download/programmer9/11929556