# Implement the Sieve of Eratosthenes and use it to find all prime numbers less than or equal to one

Implement the Sieve of Eratosthenes and use it to find all prime numbers less than or equal to one million. Use the result to

prove Goldbach's Conjecture for all even integers between four and

one million, inclusive.

Implement a method with the following declaration:

public static void sieve(int[] array);

This function takes an integer array as its argument. The array

should be initialized to the values 1 through 1000000. The

function modifies the array so that only the prime numbers remain;

all other values are zeroed out.

This function must be written to accept an integer array of any

size. You must should output for all primes numbers between 1 and

1000000, but when I test your function it may be on an array of a

different size.

Implement a method with the following declaration:

public static void goldbach(int[] array);

This function takes the same argument as the previous method

and displays each even integer between 4 and 1000000 with two

prime numbers that add to it.

The goal here is to provide an efficient implementation. This

means no multiplication, divisioni, or modulus when determining if

a number is prime. It also means that the second method must find

two primes efficiently.

Output for your program: All prime numbers between 1 and 1000000

and all even numbers between 4 and 1000000 and the two prime

numbers that sum up to it.

prove Goldbach's Conjecture for all even integers between four and

one million, inclusive.

Implement a method with the following declaration:

public static void sieve(int[] array);

This function takes an integer array as its argument. The array

should be initialized to the values 1 through 1000000. The

function modifies the array so that only the prime numbers remain;

all other values are zeroed out.

This function must be written to accept an integer array of any

size. You must should output for all primes numbers between 1 and

1000000, but when I test your function it may be on an array of a

different size.

Implement a method with the following declaration:

public static void goldbach(int[] array);

This function takes the same argument as the previous method

and displays each even integer between 4 and 1000000 with two

prime numbers that add to it.

The goal here is to provide an efficient implementation. This

means no multiplication, divisioni, or modulus when determining if

a number is prime. It also means that the second method must find

two primes efficiently.

Output for your program: All prime numbers between 1 and 1000000

and all even numbers between 4 and 1000000 and the two prime

numbers that sum up to it.

You'll get a 41.4KB .DOCX file.