## Python learning – Sieve of Eratosthenes

Get all the information about ‘Sieve of Eratosthenes’ on wikipedia (http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes). This algorithm does tell us there should be some algorithms with better time complexcity or space complexcity. Fun!

(pic took from Wikipedia)

[daveti@aimlab python]\$ cat sea.py
#!/bin/env python
# Sieve of Eratosthenes Algorithm – sea

# Input: range of number
# Output: all primes within the range
# 27SEP2012
# daveti

import math

print (“Input the range of number:”)
maxNum=int(input())

# 0 and 1 are NOT primes
isPrimeList=[ False, False]
for i in range(2, maxNum+1):
# Init the full list with True
isPrimeList.append(True)

for j in range(2, int(math.ceil(math.sqrt(maxNum)))):
if isPrimeList[ j] == True:
for k in range(j*j,(maxNum+1),j):
isPrimeList[ k] = False

# Format and print all the primes
print (“Output all the primes numbers:”)
lineList = []
numOfPrimesPerLine = 20
for m in range(maxNum+1):
if numOfPrimesPerLine == len(lineList):
print(lineList)
lineList = []
if isPrimeList[ m] == True:
lineList.append( m)

if len(lineList) != 0:
# Need to print the last line
print(lineList)
[daveti@aimlab python]\$ ./sea.py
Input the range of number:
1000
Output all the primes numbers:
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71]
[73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173]
[179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281]
[283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409]
[419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541]
[547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659]
[661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809]
[811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941]
[947, 953, 967, 971, 977, 983, 991, 997]
[daveti@aimlab python]\$