http://www.math.ucla.edu/~dinov/10a.3.01s/ |

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**HW_8_1.cpp/exe**) (The*Sieve of Eratosthenes*Algorithm) Ais any integer that is evenly divisible**prime integer**__only by itself and 1__. The*Sieve of Eratosthenes*is a method of finding prime numbers. It operates as follows:

**1.**Create an array with all elements initialized to 1 (true). Array elements with prime subscripts will remain 1. All other array elements will eventually be set to zero;

**2.**Starting with array subscript 2 (subscript 1 must be prime), every time an array element is found whose value is 1, loop through the**remainder**of the array and set to zero every element whose subscript is a multiple of the subscript for the element with value 1. For example, for array subscript 2, all elements beyond 2 in the array that are multiples of 2 will be set to zero (subscripts 4, 6, 8, 10, etc.); for array subscript 3, all elements beyond 3 in the array that are multiples of 3 will be set to zero (subscripts 6, 9, 12, 15, etc.); and so on.

When this process is complete, the array elements that are still set to one indicate that the subscript is a prime number. Finally, all subscripts for which the array elements remain equal to**1**should be printed. Write a program that uses an array of**1000**elements to determine and print the prime numbers between 1 and 999. Ignore element 0 of the array. [You should remember that*prime*numbers are the**core**of all robust public encryption systems, information encoding/decoding, just like in the example we discussed in class. The problem is that**large**primes, say of 50 digits, are__extremely__difficult to find.]

More about**Prime Numbers**could be found here!

**Sample Run:**(no user input is allowed/expected)

%>**Prime**number machine!

%> These are all prime numbers in the range [1 ; 1000]

%> 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

%> Goodbye!