primeslist is not used. Remove it from your code.
x=2: PEP 8 requires to put two spaces around the operator
Also PEP 8 complains about
while (j < primeseries):. Those parentheses (
()) are not required; remove them in order to reduce the visual clutter.
primeserieslist is misspelled: it should be
prime_series_list. Actually, the role of that very list is to hold the actual prime sieve, so why not rename it simply to
if (z <= primeseries):
if (z in primeserieslist):
could be written as
if z <= prime_series and z in prime_series_list:
SieveofEratosthenes: in Python, CamelCase identifiers are suggested to be used for naming classes. What comes to function naming, your name should be
x = x + 1: you can write more succinctly
x += 1.
z in prime_series_list run in average linear time, and, thus, are inefficient. See below for more efficient implementation.
Your implementation works and seems correct, yet there is room for improvement code style -wise and efficiency-wise:
sieve = [True for _ in range(max_integer + 1)]
sieve[0:1] = [False, False]
for start in range(2, max_integer + 1):
for i in range(2 * start, max_integer + 1, start):
sieve[i] = False
primes = 
for i in range(2, max_integer + 1):
I have set up this benchmark. From it, I get the output:
SieveofEratosthenes in 17560 milliseconds.
sieve_of_eratosthenes in 31 milliseconds.
Algorithms agree: True
Any question? Give me a message.