When this process is complete, the list elements that are still set to 1 indicate that the subscript is a prime number. These subscripts can then be printed. Write a program that uses a list of 1000 ele- ments to determine and print the prime numbers between 2 and 999. Ignore element 0 of the list.

Question

A prime integer is any integer greater than 1 that is evenly divis-
ible only by itself and 1. The Sieve of Eratosthenes is a method of finding prime numbers. It operates as follows:
a) Create a list with all elements initialized to 1 (true). List elements with prime subscripts will remain 1. All other list elements will eventually be set to zero.
b) Starting with list element 2, every time a list element is found whose value is 1, loop through the remainder of the list and set to zero every element whose subscript is a multiple of the subscript for the element with value 1. For list subscript 2, all elements beyond 2 in the list that are multiples of 2 will be set to zero (subscripts 4, 6, 8, 10, etc.); for list subscript 3, all elements beyond 3 in the list that are multiples of 3 will be set to zero (subscripts 6, 9, 12, 15, etc.); and so on.

Answer 1

```
# Sieve of Eratosthenes.

import math

total = 1000 # total number of primes to test
values = [] # holds truth/false values for primes

# add "total" 1’s to list
for i in range( 0, total + 1 ):
values.append( 1 )

# test prime values
for value in range( 2, math.sqrt( total ) ):

# test numbers not already set to 0
if values[ value ]:

# set all multiples of value to zero
multiples = range( value + value, total + 1, value )

for multiple in multiples:
values[ multiple ] = 0

# print elements set to one (prime numbers)
for value in range( 2, total + 1 ):

if values[ value ]:
print value,

print
```
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