ISC 2018 Computer Practical
Question 1
A Goldbach number is a positive even integer that can be expressed as the sum of two odd primes.
Note: All even integer numbers greater than 4 are Goldbach numbers. Example: 6 = 3 + 3
10 = 3 + 7
10 = 5 + 5
Hence, 6 has one odd prime pair 3 and 3. Similarly, 10 has two odd prime pairs, i.e. 3 and 7, 5 and 5.
Write a program to accept an even integer ‘N’ where N > 9 and N < 50. Find all the odd prime pairs whose sum is equal to the number ‘N’.
Test your program with the following data and some random data: Example 1:
INPUT: N = 14
OUTPUT: PRIME PAIRS ARE:
3, 11
7, 7
Example 2: INPUT: N = 30
OUTPUT: PRIME PAIRS ARE
7, 23
11, 19
13, 17
Example 3: INPUT: N = 17
OUTPUT: INVALID INPUT. NUMBER IS ODD.
Example 4: INPUT: N = 126
OUTPUT: INVALID INPUT. NUMBER OUT OF RANGE.
A Goldbach number is a positive even integer that can be expressed as the sum of two odd primes.
Note: All even integer numbers greater than 4 are Goldbach numbers. Example: 6 = 3 + 3
10 = 3 + 7
10 = 5 + 5
Hence, 6 has one odd prime pair 3 and 3. Similarly, 10 has two odd prime pairs, i.e. 3 and 7, 5 and 5.
Write a program to accept an even integer ‘N’ where N > 9 and N < 50. Find all the odd prime pairs whose sum is equal to the number ‘N’.
Test your program with the following data and some random data: Example 1:
INPUT: N = 14
OUTPUT: PRIME PAIRS ARE:
3, 11
7, 7
Example 2: INPUT: N = 30
OUTPUT: PRIME PAIRS ARE
7, 23
11, 19
13, 17
Example 3: INPUT: N = 17
OUTPUT: INVALID INPUT. NUMBER IS ODD.
Example 4: INPUT: N = 126
OUTPUT: INVALID INPUT. NUMBER OUT OF RANGE.
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import java.util.*;
public class Goldbach
{
boolean isPrime(int n)
{
if(n<=1) //All numbers that are less than or equal to one are non-prime
return false;
int i;
for(i=2;i<=n/2;i++)
{
if(n%i==0) //If any number between 2 and n/2 divides n then n is non prime
return false;
}
/*If any return statement is encountered it terminates the function immediately
* therefore the control will come here only when the above return statements are not executed
* which can happen only when the number is a prime number.
*/
return true;
}
void print(int n)
{
int i, j;
for(i=2;i<=n;i++)
{
for(j=i;j<=n;j++)
{
//If i and j are both prime and i+j is equal to n then i and j will be printed
if(isPrime(i)&&isPrime(j)&&i+j==n)
System.out.println(i+", "+j);
}
}
}
public static void main()
{
Scanner sc = new Scanner(System.in);
int n;
System.out.println("Enter the limit: ");
n = sc.nextInt();
if(n%2==1)
{ //Checking for invalid input and terminating the program
System.out.println("INVALID INPUT. NUMBER IS ODD.");
System.exit(0);
}
if(n<=9||n>=50)
{ //Checking for 2nd invalid input and terminating the program
System.out.println("INVALID INPUT. NUMBER OUT OF RANGE.");
System.exit(0);
}
Goldbach ob = new Goldbach(); //Creating object
System.out.println("Prime Pairs are: ");
ob.print(n);
}
}
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import java.util.*;
public class Goldbach
{
boolean isPrime(int n)
{
if(n<=1) //All numbers that are less than or equal to one are non-prime
return false;
int i;
for(i=2;i<=n/2;i++)
{
if(n%i==0) //If any number between 2 and n/2 divides n then n is non prime
return false;
}
/*If any return statement is encountered it terminates the function immediately
* therefore the control will come here only when the above return statements are not executed
* which can happen only when the number is a prime number.
*/
return true;
}
void print(int n)
{
int i, j;
for(i=2;i<=n;i++)
{
for(j=i;j<=n;j++)
{
//If i and j are both prime and i+j is equal to n then i and j will be printed
if(isPrime(i)&&isPrime(j)&&i+j==n)
System.out.println(i+", "+j);
}
}
}
public static void main()
{
Scanner sc = new Scanner(System.in);
int n;
System.out.println("Enter the limit: ");
n = sc.nextInt();
if(n%2==1)
{ //Checking for invalid input and terminating the program
System.out.println("INVALID INPUT. NUMBER IS ODD.");
System.exit(0);
}
if(n<=9||n>=50)
{ //Checking for 2nd invalid input and terminating the program
System.out.println("INVALID INPUT. NUMBER OUT OF RANGE.");
System.exit(0);
}
Goldbach ob = new Goldbach(); //Creating object
System.out.println("Prime Pairs are: ");
ob.print(n);
}
}
|
OUTPUT 1:
OUTPUT 2:
Output 3:
