sum the primes numbers below 10000 using python

Question

def is_divisible(num,prime=[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]):
    for j in prime:
        if (num % j) == 0:
            return True
    return False

first part

def find_primes(N):
    prime = [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]
    primes = []
    n = range(2,N+1)
    for num in n:
        if is_divisible(num) is False:
            primes.append(num)
    return(prime+primes)

second part

def brun(N):
    list = find_primes(N-1)
    list2 = find_primes(N)
    combs = []
    for x in list:
        for y in list2:
            if x - y ==2:
                combs.append((1/x)+(1/y))

print(brun(10000))

running this program, finally i got a none.I don't know what is wrong, please help

Answer 1

brun doesn't have a return statement, so by default it returns None . So print(brun(10000)) prints None .

Edit: Like said below, you probably want to have a return combs statement at the end of brun . However, combs is a list with N(N-1)/2 elements in it, so I doubt you want to print the whole thing. You may want to print something like

print(brun(10000)[-1])

which will print the last element of combs .

Answer 2

@Bill correctly answered your question. But let me take a moment to suggest a better algorithm; it's known as the Sieve of Eratosthenes, and was invented by a Greek mathematician over two thousand years ago. The idea is to initially mark all numbers less than n as possible primes, then for each prime, in order, to mark all of its multiples as non-primes, collecting the primes as you go:

def primes(n):
    sieve, ps = [True] * n, []
    for p in xrange(2, n):
        if sieve[p]:
            ps.append(p)
            for i in xrange(p*p, n, p):
                sieve[i] = False
    return ps

Then you can compute the sum of the primes less than n by saying sum(primes(n)) . If you're interested in programming with prime numbers, I modestly recommend this essay at my blog.