#
# 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
