给定整数n。我们需要打印1至n之间的所有双素数对。双质数是那些质数，并且两个质数之间相差两(2)的那些数。换句话说，孪生素数是素数差距为2的素数。
有时，术语“双生质”用于一对双生质。此的另一个名称是素生双胞胎或素对。通常，对(2，3)不被视为一对孪生素数。由于2是唯一的偶数质数，因此这对是唯一相差一个的质数对；因此，孪生素数与其他两个素数的间隔尽可能近。
前几个孪生素数对是：
(3, 5), (5, 7), (11, 13), (17, 19), (29, 31),
(41, 43), (59, 61), (71, 73), (101, 103),
(107, 109), (137, 139), …etc.事实：10，000以下有409个孪生素数。
例子：
Input : n = 15
Output : (3, 5), (5, 7), (11, 13)
Input : 25
Output :(3, 5), (5, 7), (11, 13), (17, 19)方法：
使用Eratosthenes筛子，找到所有小于或等于n的质数的列表，然后再次迭代列表直到n，然后检查第i个数字，如果它们均为(i + 2)个均是质数，则检查其第(i + 2)个数字，然后再打印两个数字继续至下一个数字以查找Twin prime。
C++
// C++ program print all twin primes
// using Sieve of Eratosthenes.
#include
using namespace std;
void printTwinPrime(int n)
{
// 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.
bool prime[n + 1];
memset(prime, true, sizeof(prime));
for (int p = 2; p * p <= n; p++) {
// If prime[p] is not changed,
// then it is a prime
if (prime[p] == true) {
// Update all multiples of p
for (int i = p * 2; i <= n; i += p)
prime[i] = false;
}
}
// to check for twin prime numbers
// display the twin primes
for (int p = 2; p <= n - 2; p++)
if (prime[p] && prime[p + 2])
cout << "(" << p << ", " << p + 2 << ")" ;
}
// Driver Program to test above function
int main()
{
int n = 25;
// Calling the function
printTwinPrime(n);
return 0;
} Java
// Java program to print all Twin Prime
// Numbers using Sieve of Eratosthenes
import java.io.*;
class GFG {
static void printTwinPrime(int n)
{
// 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.
boolean prime[] = new boolean[n + 1];
for (int i = 0; i <= n; i++)
prime[i] = true;
for (int p = 2; p * p <= n; p++) {
// If prime[p] is not changed,
// then it is a prime
if (prime[p] == true) {
// Update all multiples of p
for (int i = p * 2; i <= n; i += p)
prime[i] = false;
}
}
// to check for twin prime numbers
// display th twin prime
for (int i = 2; i <= n - 2; i++) {
if (prime[i] == true &&
prime[i + 2] == true)
// Display the result
System.out.print(" (" + i + ", " +
(i + 2) + ")");
}
}
// Driver Program to test above function
public static void main(String args[])
{
int n = 25;
printTwinPrime(n);
}
}Python
# Python program to illustrate...
# To print total number of twin prime
# using Sieve of Eratosthenes
def printTwinPrime(n):
# 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 + 2)]
p = 2
while (p * p <= n + 1):
# 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 * 2, n + 2, p):
prime[i] = False
p += 1
# check twin prime numbers
# display the twin prime numbers
for p in range(2, n-1):
if prime[p] and prime[p + 2]:
print("(",p,",", (p + 2), ")" ,end='')
# driver program
if __name__=='__main__':
# static input
n = 25
# Calling the function
printTwinPrime(n)C#
// C# program to illustrate..
// print all twin primes
// Using Sieve of Eratosthenes
using System;
public class GFG {
public static void printtwinprime(int n)
{
// 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.
bool[] prime = new bool[n + 1];
for (int i = 0; i < n + 1; i++)
prime[i] = true;
for (int p = 2; p * p <= n; p++) {
// If prime[p] is not changed,
// then it is a prime
if (prime[p] == true) {
// Update all multiples of p
for (int i = p * 2; i <= n; i += p)
prime[i] = false;
}
}
// check for twin prime numbers
// To display th result
for (int i = 2; i <= n - 2; i++) {
if (prime[i] == true && prime[i + 2] == true)
Console.Write(" (" + i + ", " + (i + 2) + ")");
}
}
// Driver Code
public static void Main()
{
// static input
int n = 25;
// calling the function
printtwinprime(n);
}
}PHP
Javascript
输出：
(3, 5)(5, 7)(11, 13)(17, 19)