the list of prime number in a given range python

n=int(input("Enter the number till you want to check: "))
primes = []
for i in range (2, n+1):
    for j in range(2, i):
        if i%j == 0:
            break
    else:
        primes.append(i)
print(primes)

n = 20
primes = []

for i in range(2, n + 1):
	for j in range(2, int(i ** 0.5) + 1):
 		if i%j == 0:
 			break
	else:
		primes.append(i)

print(primes)

# Python program to print all 
# prime number in an interval
#number should be greater than 1
start = 11
end = 25
 
for i in range(start,end):
  if i>1:
    for j in range(2,i):
        if(i % j==0):
            break
    else:
        print(i)

def miller_rabin(n, k):

    # Implementation uses the Miller-Rabin Primality Test
    # The optimal number of rounds for this test is 40
    # See http://stackoverflow.com/questions/6325576/how-many-iterations-of-rabin-miller-should-i-use-for-cryptographic-safe-primes
    # for justification

    # If number is even, it's a composite number

    if n == 2 or n == 3:
        return True

    if n % 2 == 0:
        return False

    r, s = 0, n - 1
    while s % 2 == 0:
        r += 1
        s //= 2
    for _ in range(k):
        a = random.randrange(2, n - 1)
        x = pow(a, s, n)
        if x == 1 or x == n - 1:
            continue
        for _ in range(r - 1):
            x = pow(x, 2, n)
            if x == n - 1:
                break
        else:
            return False
    return True

"""
a function that uses miller rabin's primality test to genarate a prime number in a certain number of bits length
in other words you give it a number of bits and you will get a prime number with that number of bits
"""
def genprimeBits(k):
    x = ""
    k = int(k)
    for y in range(k):
        x = x + "1"
    y = "1"
    for z in range(k-1):
        y = y + "0"
    x = int(x,2)
    y = int(y,2)
    p = 0
    while True:
        p = random.randrange(y,x)
        if miller_rabin(p,40):
            break
    return p

#same as other but with range not bit number
def genprimeRange(a,b):
    while True:
        p = random.randrange(a,b)
        if miller_rabin(p,40):
            break
    return p