在 all() function 中，“for”如何评估为真或假？

Question

I am working through project Euler and have made it to problem #7 . I worked out a solution with the help of a video I found online, but there is one line of code that I don't understand. Here is the problem and my solution.

"""By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13.
What is the 10 001st prime number?"""

primes = []
x = 2

while(len(primes)) < 10001:
    if all(x % prime for prime in primes):
        primes.append(x)
    x += 1

print(primes[-1])

I'm confused about the all() function. I know that x % prime will evaluate to true if the remainder is not zero, but what exactly is the function doing with the for statement? Thanks in advance!

Answer 1

The function is using list comprehension . It is taking each of the numbers from the array primes and defining them as prime . It then uses that to evaluate x % prime .

Put into a for loop x % prime for prime in primes would look like:

for prime in primes:
    return x % prime

Next, all() checks if all of them equate truthy (or true). So if one of the returns from the for loop mentioned above is false, the entire if statement returns false.