Python sieve prime numbers -

i trying sum of prime numbers using sieve on python 2.7. when run program wind 0 everytime. have no idea why happening.

import math,time  start=time.clock()  def primesieve(limit):   final=0   a=[true]*limit   a[0]=a[1]=false   i,isprime in enumerate(a):     if isprime:       n in xrange(i,limit,i):         a[n]=false   in xrange(limit):     if a[i]:         final=final+i   return final  print primesieve(2000000)  elapsed=time.clock()-start  print elapsed 

for n in xrange(i,limit,i):     a[n]=false 

it should be:

for n in xrange(2*i,limit,i):     a[n]=false 

or, more efficiently:

for n in xrange(i*i,limit, 2*i): #assuming cleared numbers     a[n]=false 

because otherwise end setting i non-prime, when prime. (the sieve should mark multiples of i non-primes, except i itself!)

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note iterating on numbers, limit, can safely stopped after reaching sqrt(limit):

import itertools  def primesieve(limit):     = [true] * limit     a[0] = a[1] = false     sqrt_limit = int(limit**0.5) + 1     predicate = lambda x: x[0] <= sqrt_limit     i, isprime in it.takewhile(predicate, enumerate(a)):         if isprime:             n in xrange(i*i, limit, i):                 a[n] = false     return sum(i i,n in enumerate(a) if n) 

the takewhile function stop iteration right after reaching square root of limit. i*i wont give errors since smaller limit.

on machine twice fast iterating on numbers.