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Program 83
Goldbach Number
Question
A Goldbach number is an even integer greater than 4 that can be expressed as the sum of two odd primes. Accept an even number and list all prime pairs whose sum is the number.
Algorithm
Step 1: Start.
Step 2: Declare the variables and data structures required for the task.
Step 3: Input N.
Step 4: Validate the input values and display an error message if they are outside the permitted range.
Step 5: Initialize the counters, flags, accumulators or result structures needed by the solution.
Step 6: Check that N is even and greater than 4.
Step 7: For each odd integer p from 3 to N/2, test whether p and N-p are prime.
Step 8: If both are prime, display the pair.
Step 9: Store the computed result and prepare it for display.
Step 10: If no pair is found, display an appropriate message.
Step 11: Stop.
Java program
Javaimport java.util.*;
class GoldbachNumber {
static boolean prime(int n) {
if (n < 2) {
return false;
}
for (int i = 2; i * i <= n; i++) {
if (n % i == 0) {
return false;
}
}
return true;
}
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
int n = sc.nextInt();
if (n <= 4 || n % 2 != 0) {
System.out.println("INVALID INPUT");
return;
}
boolean found = false;
for (int p = 3; p <= n / 2; p += 2) {
if (prime(p) && prime(n - p)) {
}
System.out.println(p + " + " + (n - p));
found = true;
}
if (!found) {
System.out.println("NO PRIME PAIR FOUND");
}
}
}Sample output
Input: 10
Output:
3 + 7
5 + 5