给定整数N。任务是找到第N个质数。
例子：
Input : 5
Output : 11
Input : 16
Output : 53
Input : 1049
Output : 8377
方法：
- 使用Eratosthenes筛子找出质数达到MAX_SIZE的数。
- 将所有素数存储在向量中。
- 对于给定的数字N，返回向量中第(N-1)个索引处的元素。
下面是上述方法的实现：
C++
// C++ program to the nth prime number
#include
using namespace std;
// initializing the max value
#define MAX_SIZE 1000005
// Function to generate N prime numbers using
// Sieve of Eratosthenes
void SieveOfEratosthenes(vector& primes)
{
// Create a boolean array "IsPrime[0..MAX_SIZE]" and
// initialize all entries it as true. A value in
// IsPrime[i] will finally be false if i is
// Not a IsPrime, else true.
bool IsPrime[MAX_SIZE];
memset(IsPrime, true, sizeof(IsPrime));
for (int p = 2; p * p < MAX_SIZE; p++) {
// If IsPrime[p] is not changed, then it is a prime
if (IsPrime[p] == true) {
// Update all multiples of p greater than or
// equal to the square of it
// numbers which are multiple of p and are
// less than p^2 are already been marked.
for (int i = p * p; i < MAX_SIZE; i += p)
IsPrime[i] = false;
}
}
// Store all prime numbers
for (int p = 2; p < MAX_SIZE; p++)
if (IsPrime[p])
primes.push_back(p);
}
// Driver Code
int main()
{
// To store all prime numbers
vector primes;
// Function call
SieveOfEratosthenes(primes);
cout << "5th prime number is " << primes[4] << endl;
cout << "16th prime number is " << primes[15] << endl;
cout << "1049th prime number is " << primes[1048];
return 0;
} Java
// Java program to the nth prime number
import java.util.ArrayList;
class GFG
{
// initializing the max value
static int MAX_SIZE = 1000005;
// To store all prime numbers
static ArrayList primes =
new ArrayList();
// Function to generate N prime numbers
// using Sieve of Eratosthenes
static void SieveOfEratosthenes()
{
// Create a boolean array "IsPrime[0..MAX_SIZE]"
// and initialize all entries it as true.
// A value in IsPrime[i] will finally be false
// if i is Not a IsPrime, else true.
boolean [] IsPrime = new boolean[MAX_SIZE];
for(int i = 0; i < MAX_SIZE; i++)
IsPrime[i] = true;
for (int p = 2; p * p < MAX_SIZE; p++)
{
// If IsPrime[p] is not changed,
// then it is a prime
if (IsPrime[p] == true)
{
// Update all multiples of p greater than or
// equal to the square of it
// numbers which are multiple of p and are
// less than p^2 are already been marked.
for (int i = p * p; i < MAX_SIZE; i += p)
IsPrime[i] = false;
}
}
// Store all prime numbers
for (int p = 2; p < MAX_SIZE; p++)
if (IsPrime[p] == true)
primes.add(p);
}
// Driver Code
public static void main (String[] args)
{
// Function call
SieveOfEratosthenes();
System.out.println("5th prime number is " +
primes.get(4));
System.out.println("16th prime number is " +
primes.get(15));
System.out.println("1049th prime number is " +
primes.get(1048));
}
}
// This code is contributed by ihritik Python3
# Python3 program to the nth prime number
primes = []
# Function to generate N prime numbers using
# Sieve of Eratosthenes
def SieveOfEratosthenes():
n = 1000005
# Create a boolean array "prime[0..n]" and
# initialize all entries it as true. A value
# in prime[i] will finally be false if i is
# Not a prime, else true.
prime = [True for i in range(n + 1)]
p = 2
while (p * p <= n):
# If prime[p] is not changed,
# then it is a prime
if (prime[p] == True):
# Update all multiples of p
for i in range(p * p, n + 1, p):
prime[i] = False
p += 1
# Print all prime numbers
for p in range(2, n + 1):
if prime[p]:
primes.append(p)
# Driver code
if __name__=='__main__':
# Function call
SieveOfEratosthenes()
print("5th prime number is", primes[4]);
print("16th prime number is", primes[15]);
print("1049th prime number is", primes[1048]);
# This code is contributed by grand_masterC#
// C# program to the nth prime number
using System;
using System.Collections;
class GFG
{
// initializing the max value
static int MAX_SIZE = 1000005;
// To store all prime numbers
static ArrayList primes = new ArrayList();
// Function to generate N prime numbers using
// Sieve of Eratosthenes
static void SieveOfEratosthenes()
{
// Create a boolean array "IsPrime[0..MAX_SIZE]"
// and initialize all entries it as true.
// A value in IsPrime[i] will finally be false
// if i is Not a IsPrime, else true.
bool [] IsPrime = new bool[MAX_SIZE];
for(int i = 0; i < MAX_SIZE; i++)
IsPrime[i] = true;
for (int p = 2; p * p < MAX_SIZE; p++)
{
// If IsPrime[p] is not changed,
// then it is a prime
if (IsPrime[p] == true)
{
// Update all multiples of p greater than or
// equal to the square of it
// numbers which are multiple of p and are
// less than p^2 are already been marked.
for (int i = p * p; i < MAX_SIZE; i += p)
IsPrime[i] = false;
}
}
// Store all prime numbers
for (int p = 2; p < MAX_SIZE; p++)
if (IsPrime[p] == true)
primes.Add(p);
}
// Driver Code
public static void Main ()
{
// Function call
SieveOfEratosthenes();
Console.WriteLine("5th prime number is " +
primes[4]);
Console.WriteLine("16th prime number is " +
primes[15]);
Console.WriteLine("1049th prime number is " +
primes[1048]);
}
}
// This code is contributed by ihritik输出：
5th prime number is 11
16th prime number is 53
1049th prime number is 8377