Print series of prime numbers in python

Question

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 ```

Accepted Answer

You need to check all numbers from 2 to n-1 (to sqrt(n) actually, but ok, let it be n). If `n` is divisible by any of the numbers, it is not prime. If a number is prime, print it.

```
for num in range(2,101):
    prime = True
    for i in range(2,num):
        if (num%i==0):
            prime = False
    if prime:
       print (num)
```

You can write the same much shorter and more pythonic:

```
for num in range(2,101):
    if all(num%i!=0 for i in range(2,num)):
       print (num)
```

As I've said already, it would be better to check divisors not from 2 to n-1, but from 2 to sqrt(n):

```
import math
for num in range(2,101):
    if all(num%i!=0 for i in range(2,int(math.sqrt(num))+1)):
       print (num)
```

For small numbers like 101 it doesn't matter, but for 10**8 the difference will be really big.

You can improve it a little more by incrementing the range you check by 2, and thereby only checking odd numbers. Like so:

```
import math
print 2
for num in range(3,101,2):
    if all(num%i!=0 for i in range(2,int(math.sqrt(num))+1)):
       print (num)
```

Edited:

As in the first loop odd numbers are selected, in the second loop no need to check with even numbers, so 'i' value can be start with 3 and skipped by 2.

```
import math
print 2
for num in range(3,101,2):
    if all(num%i!=0 for i in range(3,int(math.sqrt(num))+1, 2)):
        print (num)
```

Print series of prime numbers in python

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