Confusion with Python set()

Question

I found this code to generate prime number in Python3:

def gen_primes(N):
    """Generate primes up to N"""
    primes = set()
    for n in range(2, N):
        if all(n % p > 0 for p in primes):
            primes.add(n)
            yield n

Here I have confusion with the line if all(n % p > 0 for p in primes). Since primes is initially blank, so the code inside "if" should never execute.

To become confident, I tried the code below and it is not executing the code inside the "for".

primes = set()
n=2
print("---------Outside For Loop--------")
for p in primes:
    print("---------Inside For Loop------")
    if all(n%p>0):
        print("Hello")
    else:
        print("No Way")

So I need expert help here to understand how this prime number generator working in this case?

Look at the docs of function all when it gets empty list... – adir abargil Dec 16 '20 at 07:03 — adir abargil, Dec 16 '20 at 07:03
you can use ```help(all)``` to see the information – Zhubei Federer Dec 16 '20 at 07:06 — Zhubei Federer, Dec 16 '20 at 07:06

adir abargil · Accepted Answer · 2020-12-16T07:09:41.630

2

Your test doesn’t demonstrate the issue because the function all is what you should inspect:

all([])
>>>True

By default all return Trie for empty lists, because unless all() finds a false In a list it returns true.

edited Dec 16 '20 at 07:09

answered Dec 16 '20 at 07:04

adir abargil

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score 1 · Answer 2 · answered Dec 16 '20 at 07:46

the all() function returns True if all items in an iterable are True, otherwise it returns False. If the iterable object is empty, the all() function also returns True.

I rewrote your function by replacing all() with v (which means validity) if the number is not prime (in other words it is not divisible by any number less than the number itself) v = 0 and is not included in the primes set.

def gen_primes(N):
primes = set()

for n in range(2,N+1):

    v = 1

    for nn in range(2,n):
        if(n%nn == 0):
            v = 0
            break
    
    if v: primes.add(n)

return primes

print(gen_primes(23))

Confusion with Python set()

2 Answers2