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```#
# prime number generator
# This program gets two number as input
# and prints
#       Prime numbers in the range
#       Actual number of primes in the range
#   and Estimation based on formula
#                     n
#           pi(n)= -------
#                   log(n)
#           pi(n)=number of primes less than n
#

from math import *
def isPrime(n):
if n%2==0 and n!=2:return False    #if number is EVEN AND it is NOT 2

k = n**0.5 ;  m = ceil(k)          #if number is PERFECT SQUARE
if k==m:return False

for i in xrange(3,int(m),2):       #divisibility test ODDS ONLY
if n%i==0:return False

return True                        #otherwise it is PRIME

if __name__=='__main__':
s = input('Enter Start: ')
e = input('Enter End:   ')
s|=1                               #if s%2==0:s+=1   # ODDS only
list = [x for x in range(s,e,2) if isPrime(x)]
print list,'\n',len(list),'\n',int(ceil(e/log(e)-s/log(s)))
#prints list of primes , length of list , estimate using the formula

```

### History

• revision 2 (15 years ago)
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