I've used the pseudo code from the Wikipedia page for the Sieve of Eratosthenes.

Input: an integer n > 1

Let A be an array of Boolean values, indexed by integers 2 to n, initially all set to true.

for i = 2, 3, 4, ..., not exceeding √n:
 if A[i] is true:
 for j = i2, i2+i, i2+2i, ..., not exceeding n :
 A[j] := false

I've used the pseudo code from the Wikipedia page for the Sieve of Eratosthenes.

Input: an integer n > 1

Let A be an array of Boolean values, indexed by integers 2 to n, initially all set to true.

for i = 2, 3, 4, ..., not exceeding √n:
 if A[i] is true:
 for j = i^2, i^2+i, i^2+2i, ..., not exceeding n :
 A[j] := false

Here is a solution for problem #7 on projecteuler.net

By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13. What is the 10,001st prime number?

I used the pseudo code from the wikipedia page for the Sieve of Eratosthenes.

Input: an integer n > 1
Let A be an array of Boolean values, indexed by integers 2 to n, initially all set to true.
for i = 2, 3, 4, ..., not exceeding √n:
 if A[i] is true:
 for j = i2, i2+i, i2+2i, ..., not exceeding n :
 A[j] := false
---------------------------------------------------------------------------------

Here is a solution for Project Euler Problem #7.

By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13. What is the 10,001st prime number?

I've used the pseudo code from the Wikipedia page for the Sieve of Eratosthenes.

Input: an integer n > 1

Let A be an array of Boolean values, indexed by integers 2 to n, initially all set to true.

for i = 2, 3, 4, ..., not exceeding √n:
 if A[i] is true:
 for j = i2, i2+i, i2+2i, ..., not exceeding n :
 A[j] := false

Here is a solution for problem #7 on projecteuler.net
By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th 
prime is 13.
What is the 10,001st prime number?
I used the pseudo code from the wikipedia page for the Sieve of Eratosthenes.
Input: an integer n > 1
Let A be an array of Boolean values, indexed by integers 2 to n,initially all set to true.
for i = 2, 3, 4, ..., not exceeding √n:
 if A[i] is true:
 for j = i2, i2+i, i2+2i, ..., not exceeding n :
 A[j] := false
------------------------------------------------------------------------------------------
import java.util.*;
public class FindPrimesHashMap {
 public static void getPrime(int x) {
 int n = (x * ((int)Math.sqrt(x) / 10)) + x;
 int nSqrt = (int)Math.floor(Math.sqrt(n));
 int j = 0;
 int k = 0;
 Map<Integer, Boolean> primeMap = new HashMap<Integer, Boolean>();
 Set<Map.Entry<Integer, Boolean>> primes = primeMap.entrySet();
 ArrayList<Integer> primeArray = new ArrayList<Integer>();
 for (int a = 2; a < n; a++) {
 primeMap.put(a, true);
 }
 for (int i = 2; i <= nSqrt; i++) {
 if (primeMap.get(i)) {
 while (true) {
 j = (i * i) + (k * i);
 k++;
 if (j > n) {
 break;
 }
 primeMap.put(j, false);
 }
 j = 0;
 k = 0;
 }
 } 
 for (Map.Entry<Integer, Boolean> entry : primes) {
 if (entry.getValue()) {
 primeArray.add(entry.getKey());
 }
 }
 Collections.sort(primeArray);
 System.out.println(primeArray.get(x - 1));
}

Here is a solution for problem #7 on projecteuler.net

By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13. What is the 10,001st prime number?

I used the pseudo code from the wikipedia page for the Sieve of Eratosthenes.

Input: an integer n > 1
Let A be an array of Boolean values, indexed by integers 2 to n,initially all set to true.
for i = 2, 3, 4, ..., not exceeding √n:
 if A[i] is true:
 for j = i2, i2+i, i2+2i, ..., not exceeding n :
 A[j] := false
---------------------------------------------------------------------------------

Any suggestions would be much appreciated.

import java.util.*;
public class FindPrimesHashMap {
 public static void getPrime(int x) {
 int n = (x * ((int)Math.sqrt(x) / 10)) + x;
 int nSqrt = (int)Math.floor(Math.sqrt(n));
 int j = 0;
 int k = 0;
 Map<Integer, Boolean> primeMap = new HashMap<Integer, Boolean>();
 Set<Map.Entry<Integer, Boolean>> primes = primeMap.entrySet();
 ArrayList<Integer> primeArray = new ArrayList<Integer>();
 for (int a = 2; a < n; a++) {
 primeMap.put(a, true);
 }
 for (int i = 2; i <= nSqrt; i++) {
 if (primeMap.get(i)) {
 while (true) {
 j = (i * i) + (k * i);
 k++;
 if (j > n) {
 break;
 }
 primeMap.put(j, false);
 }
 j = 0;
 k = 0;
 }
 } 
 for (Map.Entry<Integer, Boolean> entry : primes) {
 if (entry.getValue()) {
 primeArray.add(entry.getKey());
 }
 }
 Collections.sort(primeArray);
 System.out.println(primeArray.get(x - 1));
}