寻找关于这个“for-loop”如何工作的澄清

Question

我是一个完整的编程初学者，所以请原谅我的天真。

我想用Python制作一个程序，让我打印给定的n数量的素数，其中n由用户输入。我搜索了一下“for/while”循环，并做了一些修补。我运行了一个我在网上看到的程序，并修改了它来适应这个问题。代码如下：

i = 1

print("Hi! Let's print the first N prime numbers.")
nPrimes = int(input("Enter your N: "))

counter =  0

while True:
    c = 0 #another initialization
    for x in range (1, (i + 1)):
        a = i % x # "a" is a new variable that got introduced.
        if a == 0:
            c = c + 1
    if c == 2:
        print(i, end = "  ")
        counter = counter + 1
        if counter > = nPrimes: #if it reaches the number input, the loop will end.
            break
    i = i+1

print(":  Are your", nPrimes, "prime number/s!")
print()
print("Thanks for trying!")

如有任何澄清，将不胜感激。太感谢你们了！

Answer 1

从维基百科我们知道：

质数（或素数）是一个大于1的自然数，不能由两个较小的自然数相乘而成。

所以求一个素数，就是求一个自然数，也就是一个整数，它只能被1或它本身整除。这被称为定义法来寻找素数。

for x in range (1, (i + 1)):
    a = i % x # "a" is a new variable that got introduced.
    if a == 0:
        c = c + 1

if c == 2:
    print(i, end = "  ")
    counter = counter + 1
    if counter > = nPrimes: #if it reaches the number input, the loop will end.
        break

# Start from 2 instead of 1
# and end at `i - 1` instead of `i`
for x in range (2, i):
    a = i % x # "a" is a new variable that got introduced.
    if a == 0:
        c = c + 1

    # Abandon the loop
    # because an integer with factors other than 1 and itself
    # is unevitably a composite number, not a prime
    if c > 0:
        break

if c == 0:
    print(i, end = "  ")
    counter = counter + 1
    if counter >= nPrimes: #if it reaches the number input, the loop will end.
        break

#if it reaches the number input, the loop will end.
while counter < nPrimes:
    c = 0 #another initialization

    # Start from 2 instead of 1
    # and end at `i - 1` instead of `i`
    for x in range (2, i):
        a = i % x # "a" is a new variable that got introduced.
        if a == 0:
            c = c + 1

        # Abandon the loop
        # because an integer with factors other than 1 and itself
        # is unevitably a composite number, not a prime
        if c > 0:
            break

    if c == 0:
        print(i, end = "  ")
        counter = counter + 1

    i = i + 1

如果您想了解更多关于如何提高程序查找素数的效率的信息，请阅读C语言中的这段代码。：P