Print series of prime numbers in python

Question

I am trying to learn Python programming, and I'm pretty new at this.

I was having issues in printing a series of prime numbers from one to hundred. I can't figure our what's wrong with my code.

Here's what I wrote; it prints all the odd numbers instead of primes:

for num in range(1,101):
    for i in range(2,num):
        if (num%i==0):
            break
        else:
            print(num)
            break

Answer 1

A simpler and more efficient way of solving this is storing all prime numbers found previously and checking if the next number is a multiple of any of the smaller primes.

n = 1000
primes = [2]

for i in range(3, n, 2):
    if not any(i % prime == 0 for prime in primes):
        primes.append(i)

print(primes)

Note that any is a short circuit function, in other words, it will break the loop as soon as a truthy value is found.

Answer 2

This is a sample program I wrote to check if a number is prime or not.

def is_prime(x):
    y=0
    if x<=1:
        return False
    elif x == 2:
        return True
    elif x%2==0:
        return False
    else:
        root = int(x**.5)+2
        for i in xrange (2,root):
            if x%i==0:
                return False
                y=1
        if y==0:
            return True

Answer 3

I'm a proponent of not assuming the best solution and testing it. Below are some modifications I did to create simple classes of examples by both @igor-chubin and @user448810. First off let me say it's all great information, thank you guys. But I have to acknowledge @user448810 for his clever solution, which turns out to be the fastest by far (of those I tested). So kudos to you, sir! In all examples I use a values of 1 million (1,000,000) as n.

Please feel free to try the code out.

Good luck!

Method 1 as described by Igor Chubin:

def primes_method1(n):
    out = list()
    for num in range(1, n+1):
        prime = True
        for i in range(2, num):
            if (num % i == 0):
                prime = False
        if prime:
            out.append(num)
    return out

Benchmark: Over 272+ seconds

Method 2 as described by Igor Chubin:

def primes_method2(n):
    out = list()
    for num in range(1, n+1):
        if all(num % i != 0 for i in range(2, num)):
            out.append(num)
    return out

Benchmark: 73.3420000076 seconds

Method 3 as described by Igor Chubin:

def primes_method3(n):
    out = list()
    for num in range(1, n+1):
        if all(num % i != 0 for i in range(2, int(num**.5 ) + 1)):
            out.append(num)
    return out

Benchmark: 11.3580000401 seconds

Method 4 as described by Igor Chubin:

def primes_method4(n):
    out = list()
    out.append(2)
    for num in range(3, n+1, 2):
        if all(num % i != 0 for i in range(2, int(num**.5 ) + 1)):
            out.append(num)
    return out

Benchmark: 8.7009999752 seconds

Method 5 as described by user448810 (which I thought was quite clever):

def primes_method5(n):
    out = list()
    sieve = [True] * (n+1)
    for p in range(2, n+1):
        if (sieve[p]):
            out.append(p)
            for i in range(p, n+1, p):
                sieve[i] = False
    return out

Benchmark: 1.12000012398 seconds

Notes: Solution 5 listed above (as proposed by user448810) turned out to be the fastest and honestly quiet creative and clever. I love it. Thanks guys!!

EDIT: Oh, and by the way, I didn't feel there was any need to import the math library for the square root of a value as the equivalent is just (n**.5). Otherwise I didn't edit much other then make the values get stored in and output array to be returned by the class. Also, it would probably be a bit more efficient to store the results to a file than verbose and could save a lot on memory if it was just one at a time but would cost a little bit more time due to disk writes. I think there is always room for improvement though. So hopefully the code makes sense guys.

Answer 4

Here is the simplest logic for beginners to get prime numbers:

p=[]
for n in range(2,50):
    for k in range(2,50):
        if n%k ==0 and n !=k:
            break
        else:
            for t in p:
                if  n%t ==0:
                    break
            else:
                p.append(n)

print p

Answer 5

How about this? Reading all the suggestions I used this:

prime=[2]+[num for num in xrange(3,m+1,2) if all(num%i!=0 for i in range(2,int(math.sqrt(num))+1))]

Prime numbers up to 1000000

root@nfs:/pywork# time python prime.py

78498

real 0m6.600s

user 0m6.532s

sys 0m0.036s

Answer 6

f=0
sum=0
for i in range(1,101):
    for j in range(1,i+1):
        if(i%j==0):
            f=f+1
    if(f==2):
        sum=sum+i
        print i        
    f=0
print sum