Efficient Way To Find Primes And Sum Of Primes

Jan 11, 2014

Java Code:

class Program {
public static void main (String[] args) {
long max = 200; //add up all primes up to 200
long ans = 0;
for(long x = 2; x < max; x++) {
if(isPrime(x)) {
ans += x;

[Code] ....

This code adds up all of the primes before a certain number (max). Unfortunately, it is much too slow when you get up to bigger numbers - how can I do this more efficiently.

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Implement Class That Computes All Primes Up To Some Integer N

Feb 5, 2014

I am working on a problem that computes primes. Here is the problem: You are going to implement a class that computes all the primes up to some integer n. The technique you are to use was developed by a Greek named Eratosthenes who lived in the third century BC. The technique is known as the Sieve of Eratosthenes. The algorithm is described by the following pseudocode:

create a queue and fill it with the consecutive integers 2 through n inclusive.
create an empty queue to store primes.
do {
obtain the next prime p by removing the first value in the queue of numbers.
put p into the queue of primes.
go through the queue of numbers, eliminating numbers divisible by p.
} while (p < sqrt(n))
all remaining values in numbers queue are prime, so transfer them to primes queue

You are to use the Queue interface provided. When you want to construct a Queue object, you should make it of type LinkedQueue. These classes are included. You should define a class called Sieve with the following public methods:

Sieve() - Constructs a sieve object.

void computeTo(int n) - This is the method that should implement the sieve algorithm. All prime computations must be implemented using this algorithm. The method should compute all primes up to and including n. It should throw an IllegalArgumentException if n is less than 2.

void reportResults() - This method should report the primes to System.out. It should throw an IllegalStateException if no legal call has been made yet on the computeTo method. It is okay for it to have an extra space at the end of each line.

int getMax() - This is a convenience method that will let the client find out the value of n that was used the last time computeTo was called. It should throw an IllegalStateException if no legal call has been made yet on the computeTo method.

int getCount() - This method should return the number of primes that were found on the last call on computeTo. It should throw an IllegalStateException if no legal call has been made yet on the computeTo method.

Your reportResults method should print the maximum n used and should then show a list of the primes, 12 per line with a space after each prime. Notice that there is no guarantee that the number of primes will be a multiple of 12. The calls on reportResults must exactly reproduce the format of the sample log. The final line of output that appears in the log reporting the percentage of primes is generated by the main program, not by the call on reportResults.

Here is my class Sieve. I am having difficulty getting all the primes into the proper queue:

public class Sieve {
private Queue<Integer> primes;
private Queue<Integer> numList;
private boolean computed = false;
private int max;
private int count = 0;

[Code] ....

When I input say, 20, I only get 2, 3, and 11 back as primes. Somewhere in the algorithm (lines 40-54) I seem to have gone awry, but I'm not certain where. Here are the other classes:

SieveMain:
// This program computes all the prime numbers up to a given integer n. It uses the classic "Sieve of Eratosthenes" to do so.

import java.util.*;
public class SieveMain {
public static void main(String[] args) {
System.out.println("This program computes all prime numbers up to a");
System.out.println("maximum using the Sieve of Eratosthenes.");
System.out.println();

[Code] .....