Question

def all_primes(start,end):
    list_nonprimes = []
    list_primes = []

    for i in range(start,end):
        for a in range(2,i):
            if i % a == 1 and i not in list_nonprimes:
                if i not in list_primes:
                    list_primes.append(i)
            else:
                list_nonprimes.append(i)

    return list_primes

为什么这会给我一个不正确的输出？

>>> all_primes(1,10)
[3,5,7,9]

如何消除9？

Answer 1

有一种更简单的方法可以做到这一点，因为您已经固有地生成了少于您当前正在检查的数字的素数列表：

def all_primes(start,end):
    list_primes = []

    for i in range(2,end):
        for a in list_primes:
            if i % a == 0:
                break
        else:
            list_primes.append(i)

    return [x for x in list_primes if x >= start]

理解这一点的关键是了解for...else构造在Python中的工作原理。从本质上讲，for循环可以有else语句，只有在循环评估期间没有运行break语句时才会执行该语句。

Answer 2

从以下位置更改：

        if i % a == 1 and i not in list_nonprimes:
            if i not in list_primes:
                list_primes.append(i)
        else:
            list_nonprimes.append(i)

为：

        if i % a == 0 and i not in list_primes:
            if i not in list_nonprimes:
                list_nonprimes.append(i)
        else:
            list_primes.append(i)

除此之外：您还可以考虑实施Sieve of Eratosthenes。理解并且效率更高，这是非常直接的。

Answer 3

我尝试检查你的代码，看看你哪里出错了，但最后做了一些改变和优化。我对代码进行了评论，希望它能够解释自己。

def all_primes(start,end):
    list_nonprimes = []
    list_primes = []

    for i in range(start,end):
        # if already present in non_primes, skip
        if i in list_nonprimes: continue

        # if already present in primes, skip
        if i in list_primes: continue

        # if 2, mark it as prime. Special case
        if i == 2 :
            list_primes.append(i)
            continue

        # even numbers are not prime
        if i%2 == 0: 
            list_nonprimes.append(i)
            continue

        # only check divisibility with odd numbers starting at 3
        # and ending at sqrt(i)
        for a in range(3,int(i**0,5)+1,2):
            if i % a == 0 :
                list_nonprimes.append(i)
                break

        # if we got here, and the number wasn;t added to non_primes
        # it must be a prime
        if i not in list_nonprimes: list_primes.append(i)            

    return list_primes

start = 2
end = 10
print all_primes(start, end)

Demo

如何获得某一组的所有素数？

3 个答案: