Please, submit your homework electronically using the "submit" system.
Please try to follow the "good programming" conventions
we discussed in class. Write modular code and include all
of your functions in the same CPP file as your main.
(The Sieve of Eratosthenes Algorithm)
A prime integer is any integer that is evenly
divisible 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.]