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segmentedSieve.py
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segmentedSieve.py
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import time
import math
import memory_profiler as mem_profile
def eratosthenesSieve(limit):
markArr = [True for i in range(limit)]
for p in range(2, limit - 1):
if not markArr[p]:
continue
inc = p
inc += p
while inc < limit:
markArr[inc] = False
inc += p
prime = []
for i in range(len(markArr)):
if markArr[i]:
prime.append(i)
return prime
def segmentedSieve(n):
limit = n // 4
# Create prime array to start
prime = eratosthenesSieve(limit)
# Remove 0 and 1 from prime Array
prime.remove(prime[0])
prime.remove(prime[0])
# Segment Start
low = limit + 1
while low <= n:
markArr = [True for i in range(limit)]
for p in prime:
if p > math.sqrt(low + limit + 1):
break
startP = (low // p) * p
if startP < low:
startP += p
markX = startP - low
while markX <= len(markArr) - 1:
markArr[markX] = False
markX += p
for i in range(len(markArr)):
if markArr[i]:
prime.append(i + low)
low += limit
# print(prime)
print(len(prime))
print('Memory before: {}Mb'.format(mem_profile.memory_usage()))
start = time.perf_counter()
segmentedSieve(10000000) # Old code did 100000 in ~ 4, 1000000 ~ 40+
end = time.perf_counter()
print(f"Primes calculated in {end - start:0.4f} seconds")
print('Memory After: {}Mb'.format(mem_profile.memory_usage()))
#
# 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
# 1, 2, 3, 4, 5, 6, 7, 8, 9, 10