"""     The Sieve of Eratosthenes implemented in Python

        Robin Broad

        May 2018

        Part of a project to demonstrate an ability to

        implement an algorithm in a range of different

        computing languages and to use a range of

        compilers, including the following:

        Java: BlueJ

        C: Miracle C

        C++: Microsoft Visual C++.NET/ GNU GCC/ Linux Code::Blocks IDE

        C#: Microsoft Visual C#.NET

        Visual Basic: Microsoft Visual Basic.NET

        Python: Linux Ninja Python IDE

"""

import math #Import math module

import sys #Import system-specific parameters and functions - used in print formatting here

#variable declarations/ initialisation

RANGE=1000 #we are calculating the prime numbers up to this number

listOfIntegers=[0]*(RANGE+1)    #This array of integers will hold all the numbers up to the value of RANGE

                                #Notice that RANGE+1 has been used so that we can use the array in the range

                                #1->RANGE to simplify the coding of the algorithm

root=int(math.sqrt(RANGE))      #needed later on when removing multiples, casting is used since we're

                                #only interested in integer values

#initialising the integer list/ collection (array)

for n in range(1, RANGE+1):

        listOfIntegers[n]=n

#starting from n=2, "remove" multiples of n up the value of RANGE

#repeat for increasing values of n up to the square root of RANGE

#delete (mark as zero) the multiples of n

for n in range(2, root):

        multiplier=2

        while multiplier*n<=RANGE: # while loop used as Python for loop does not have a test condition

                product=n*multiplier

                listOfIntegers[product]=0 #marked as zero means that it is not a prime number

                multiplier +=1

#print out the prime numbers remaining, remembering that 2 is the first prime number

print("The Sieve of Eratosthenes program")

print("Written in Python using Linux Ninja IDE")

print("Robin Broad, May 2018.\n")

print("The prime numbers in the range: 1 to %s are:-" % RANGE)

for n in range(1, RANGE):

        #print all non-zero elements of the integer array

        if listOfIntegers[n]!=0:

                #print(listOfIntegers[n]) - command not suitable, see below

                sys.stdout.write("%s " % listOfIntegers[n])     #sys.stdout.write() is used here as print() produces

                                                                #a newline afer each number which was not wanted

print("\nEnd of Program.")

"""

This program produced the following output:

The Sieve of Eratosthenes program

Written in Python using Linux Ninja IDE

Robin Broad, May 2018.

The prime numbers in the range: 1 to 1000 are:-

1 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 283 293 307 311 313 317 331 337 347 349 353 359 367 373 379 383 389 397 401 409 419 421 431 433 439 443 449 457 461 463 467 479 487 491 499 503 509 521 523 541 547 557 563 569 571 577 587 593 599 601 607 613 617 619 631 641 643 647 653 659 661 673 677 683 691 701 709 719 727 733 739 743 751 757 761 769 773 787 797 809 811 821 823 827 829 839 853 857 859 863 877 881 883 887 907 911 919 929 937 941 947 953 961 967 971 977 983 991 997

End of Program.

"""