Primzahlzwillinge
Ein Primzahlzwilling sind solche Zahlen, die Primzahlen sind und zwischen den beiden Primzahlen eine Differenz von zwei ( 2 ) haben. Mit anderen Worten, ein Primzahlzwilling ist eine Primzahl, die eine Primzahllücke von zwei hat.
Manchmal wird der Begriff Primzahlenzwilling für ein Paar Primzahlzwillinge verwendet; ein alternativer Name dafür ist Prime Twin oder Prime Pair. Normalerweise wird das Paar (2, 3) nicht als Paar von Primzahlzwillingen betrachtet. Da 2 die einzige gerade Primzahl ist, ist dieses Paar das einzige Paar von Primzahlen, die sich um eins unterscheiden; Daher sind Primzahlzwillinge für zwei andere Primzahlen so eng wie möglich beabstandet.
Die ersten paar Primzahlzwillinge sind:
(3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), (59, 61), (71, 73), (101, 103), (107, 109), (137, 139), …etc.
FAKT : Es gibt 409 Primzahlzwillinge unter 10.000.
Jedes Primzahlzwillingspaar außer (3, 5) hat die Form (6n – 1, 6n + 1) für eine natürliche Zahl n; das heißt, die Zahl zwischen den beiden Primzahlen ist ein Vielfaches von 6.
Beispiele:
Input : n1 = 11, n2 = 13 Output : Twin Prime Input : n1 = 23, n2 = 37 Output : Not Twin Prime
Voraussetzung: Primzahltest | Set 1 (Einführung und Schulmethode)
C++
// CPP program to check twin prime
#include <iostream>
using namespace std;
// Please refer below post for details of this
// function
// https://goo.gl/Wv3fGv
bool isPrime(int n)
{
// Corner cases
if (n <= 1) return false;
if (n <= 3) return true;
// This is checked so that we can skip
// middle five numbers in below loop
if (n%2 == 0 || n%3 == 0) return false;
for (int i=5; i*i<=n; i=i+6)
if (n%i == 0 || n%(i+2) == 0)
return false;
return true;
}
// Returns true if n1 and n2 are twin primes
bool twinPrime(int n1, int n2)
{
return (isPrime(n1) && isPrime(n2) &&
abs(n1 - n2) == 2);
}
// Driver code
int main()
{
int n1 = 11, n2 = 13;
if (twinPrime(n1, n2))
cout << "Twin Prime" << endl;
else
cout << endl
<< "Not Twin Prime" << endl;
return 0;
}
Java
// JAVA Code for Twin Prime Numbers
import java.util.*;
class GFG {
// Please refer below post for
// details of this function
// https://goo.gl/Wv3fGv
static boolean isPrime(int n)
{
// Corner cases
if (n <= 1) return false;
if (n <= 3) return true;
// This is checked so that we can skip
// middle five numbers in below loop
if (n % 2 == 0 || n % 3 == 0)
return false;
for (int i = 5; i * i <= n; i = i + 6)
if (n % i == 0 || n % (i + 2) == 0)
return false;
return true;
}
// Returns true if n1 and n2 are twin primes
static boolean twinPrime(int n1, int n2)
{
return (isPrime(n1) && isPrime(n2) &&
Math.abs(n1 - n2) == 2);
}
/* Driver program to test above function */
public static void main(String[] args)
{
int n1 = 11, n2 = 13;
if (twinPrime(n1, n2))
System.out.println("Twin Prime");
else
System.out.println("Not Twin Prime");
}
}
// This code is contributed by Arnav Kr. Mandal.
Python3
# Python3 code to check twin prime
import math
# Function to check whether a
# number is prime or not
def isPrime( n ):
# Corner cases
if n <= 1:
return False
if n <= 3:
return True
# This is checked so that we
# can skip middle five numbers
# in below loop
if n%2 == 0 or n%3 == 0:
return False
for i in range(5, int(math.sqrt(n)+1), 6):
if n%i == 0 or n%(i + 2) == 0:
return False
return True
# Returns true if n1 and n2 are
# twin primes
def twinPrime(n1 , n2):
return (isPrime(n1) and isPrime(n2) and
abs(n1 - n2) == 2)
# Driver code
n1 = 137
n2 = 139
if twinPrime(n1, n2):
print("Twin Prime")
else:
print("Not Twin Prime")
# This code is contributed by "Sharad_Bhardwaj".
C#
// C# Code for Twin Prime Numbers
using System;
class GFG {
// Please refer below post for
// details of this function
// https://goo.gl/Wv3fGv
static bool isPrime(int n)
{
// Corner cases
if (n <= 1) return false;
if (n <= 3) return true;
// This is checked so that we can skip
// middle five numbers in below loop
if (n % 2 == 0 || n % 3 == 0)
return false;
for (int i = 5; i * i <= n; i = i + 6)
if (n % i == 0 || n % (i + 2) == 0)
return false;
return true;
}
// Returns true if n1 and n2 are twin primes
static bool twinPrime(int n1, int n2)
{
return (isPrime(n1) && isPrime(n2) &&
Math.Abs(n1 - n2) == 2);
}
// Driver program
public static void Main()
{
int n1 = 11, n2 = 13;
if (twinPrime(n1, n2))
Console.WriteLine("Twin Prime");
else
Console.WriteLine("Not Twin Prime");
}
}
// This code is contributed by vt_m.
PHP
<?php
// PhP program to check twin prime
// Please refer below post for details
// of this function
// https://goo.gl/Wv3fGv
function isPrime($n)
{
// Corner cases
if ($n <= 1) return false;
if ($n <= 3) return true;
// This is checked so that we can skip
// middle five numbers in below loop
if ($n % 2 == 0 || $n % 3 == 0)
return false;
for ($i = 5; $i * $i <= $n; $i = $i + 6)
if ($n % $i == 0 || $n % ($i + 2) == 0)
return false;
return true;
}
// Returns true if n1 and n2 are twin primes
function twinPrime($n1, $n2)
{
return (isPrime($n1) && isPrime($n2) &&
abs($n1 - $n2) == 2);
}
// Driver code
$n1 = 11; $n2 = 13;
if (twinPrime($n1, $n2))
echo "Twin Prime", "\n";
else
echo "\n", "Not Twin Prime", "\n";
// This code is contributed by ajit
?>
Javascript
<script>
// javascript Code for Twin Prime Numbers
// Please refer below post for
// details of this function
// https://goo.gl/Wv3fGv
function isPrime( n)
{
// Corner cases
if (n <= 1)
return false;
if (n <= 3)
return true;
// This is checked so that we can skip
// middle five numbers in below loop
if (n % 2 == 0 || n % 3 == 0)
return false;
for ( let i = 5; i * i <= n; i = i + 6)
if (n % i == 0 || n % (i + 2) == 0)
return false;
return true;
}
// Returns true if n1 and n2 are twin primes
function twinPrime( n1, n2) {
return (isPrime(n1) && isPrime(n2) && Math.abs(n1 - n2) == 2);
}
/* Driver program to test above function */
let n1 = 11, n2 = 13;
if (twinPrime(n1, n2))
document.write("Twin Prime");
else
document.write("Not Twin Prime");
// This code is contributed by gauravrajput1
</script>
Ausgabe :
Twin Prime