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Q:

# 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)``````
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``````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)``````
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``````# 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)
``````
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``````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
``````
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