Have a good evening!

**The Aim:** to obtain a Sieve of Erastothenes

**The Means:** to build a function of a number n that the prime numbers up to n.

**The code** supposed to make this

```
from math import sqrt
def holeofStrainer():
"""The purpose is to build a sieve of Erasthotenes.
We beginn with a sieve without holes, called biglist.
The indexes of the list have a double function:
First, The natural list indexation. II-st, there are
as keys of the corresponding list items(the boolean
values of the prime being question about each number).
We have for each index a"""
bigList = [False, False] + [True]*100
print("line 11 - bigList : ", bigList)
for num in range(3, 101):
print("line 13 - num : ", num)
# I f we don't find divisors of nume littler that sqrt(num)
# it is guaranted that num is prime.
# 'int(sqrt(num)) + 1' is the first integer greater than sqrt(num)
for x in range(bigList[2], bigList[int(sqrt(num)) + 1]):
print("line 18 x is equal to %d"%x)
if num % x == 0:
print("line 20 {0} divided by {1} = {2} ".format(num, x, num/x))
bigList[num] == False
print ("bigList index {0} == {1}".format(num, bigList[num]))
bigList[num] == True
for multiple in range (2, int(101/num) + 1):
bigList[multiple] = False
return(bigList) #We expect a 'sieve with many holes'
print("the last result of bigList {} ".format(holeofStrainer()))
```

**The wished unrolling of the code**

line 11 biglist [False, False, True …...True]

line 13 num 3

line 18 x :2

line 20: 3 divided by 2 is equal to 1.5

biglist index 3 == True

line 13 num 4

line 18 x:2

line 20 4 divided by 2 is equal to 2

biglist index 4 == False

The disapointing **output:**

```
line 11 - bigList : [False, False, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True]
the last result of bigList [False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, False, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True, True]
```

**The request.**

Where is the obvious lack of understanding in the loop principle?

If that is a tutorial that reffers directly to this kind of error, it is welcome.