Python finding Prime Numbers between any two numbers -

i'm trying find prime numbers between 2 random numbers.

firstly, have written code like:

m,n = map(int, raw_input().split()) in range(m, n+1):     j in range(2, i):         if i%j == 0:             break     else:         print i, 

now test case suppose enter 2, 30 prints

2 3 5 7 11 13 17 19 23 29

now analyzing, don't need loop till "i" in second loop rather can same looping till i/2, changed code as:

m,n = map(int, raw_input().split()) in range(m, n+1):     j in range(2, int(i/2)+1):         if i%j == 0:             break     else:         print i, 

then result same above while looped till i/2 in second loop.

now, i'm trying use sieve of eratosthenes method print prime numbers , used code as:

m,n = map(int, raw_input().split()) in range(m, n+1):     sqrt_num = int(n**(0.5))     j in range(2, sqrt_num+1):         if i%j == 0:             break     else:         print i, 

but prints

7 11 13 17 19 23 29

for same input.

please me understand doing wrong. , how can accomplish same using method.

your inner loop used loop until i-1 or i/2. inner loop short when i small, , longer when i got larger.

now, inner loop goes sqrt_num, constant computed n. difference in behavior.

consider i = 3, inner loop runs j = 2 j = 5, , find case i%j == 0 ... specifically, when j == 3.

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to clear: problem "sqrt_num, constant". change square root of outer index, i.

    sqrt_num = int(i**(0.5))