Primes A prime number is an integer that has exactly two factors: one, and itsel

Question

Primes

A prime number is an integer that has exactly two factors: one, and itself. The number 1, however, is not considered to be prime. So the first few prime numbers are 2, 3, 5, 7, 11, 13.

Define a helper function using the symbolic operator notation slash-question-mark: (/?). This can be used as an infix operator to determine whether a number is divisible by another number (with no remainder). It returns a Boolean. For example:

ghci> 3 /? 2

False

ghci> 18 /? 3

True

ghci> 18 /? 4

False

Next, you can define isPrime n. It can check whether any number in the range [2..n-1] divides n. (It also must ensure that n > 1.)

Finally, a twin prime is a pair of neighboring odd numbers that are both primes. For example 11 and 13 are both prime so they are referred to as twins. Define a function isFirstTwinPrime n that determines whether n is the first of a pair of twin primes.

Explanation / Answer

# Checks prime numbers and returns twin prime numbers if they are.

// Author:dhanaji waghmare
import java.util.*;
class PrimeNumberCode {
  
static boolean isPrime(int n)  
{
if (n <= 1) return false;
if (n <= 3) return true;

if (n /? 2 || n /? 3 )  
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);
}

public static void main(String[] args)  
{
int n1 = 11, n2 = 13;
  
if (twinPrime(n1, n2))
System.out.println(" This are Twin Prime numbers");
else
System.out.println("These are Not Twin Prime numbers");
}
}

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.