Python挑战: distinct combination of prime numbers in a given range

Question

考虑这个挑战:

Given two numbers A and B, in how many ways you can select B distinct primes, where each of the primes should be less than or equal to A (<= A). Since the number can be large, provide your answer mod 65537.

例如

如果A = 7和B = 2 ，那么:
所有素数 <= A是 {2, 3, 5, 7} ，答案将是 6 :{2, 3} {2, 5} {2, 7} {3, 5} {3, 7} {5, 7}

我创建了这个解决方案:

from math import factorial
from math import fmod 

def nPk(n,k):
    return int( factorial(n)/factorial(n- k))  

def is_prime(a):
    for i in range(2,a):
        if a % i ==0:
            return False
    return True

def distinct_primes(A):
    primes = []
    for i in range(2,A):
        if is_prime(i):
            primes.append(i)
    return len(primes)

def fct(A, B):
    return nPk(distinct_primes(A),B)

#print fct(59,5)% 65537
print fmod(fct(69,8), 65537)

但是，我没有得到正确的答案!我在这里缺少什么？

Answer 1

Ionut 关于包容性问题的说法是正确的!
除此之外，您应该将 nPk 定义更改为:

def nPk(n,k):
    return int( factorial(n)/(factorial(n- k) * factorial(k)))