Printing Prime Number Patterns in C | Conditional Patterns

Integrating algorithmic checks into nested loops elevates basic pattern programming into advanced problem-solving. Today’s article in our Pattern Programming in C series covers the Prime Number Triangle Pattern. This tutorial demonstrates how to combine nested loop structures with primality testing logic to display prime numbers in a triangular arrangement.

Pattern Title: Prime Number Right Triangle Pattern in C

Purpose: Strengthen your nested loop logic, conditional reasoning, and prime-checking algorithms.

Prerequisites: Knowledge of basic for loops, printf, scanf, custom functions, and if-else control flow.

Final Output

For an input of rows = 4, the program generates:

2

3 5
7 11 13
17 19 23 29

Deconstructing the Pattern: The Logic

Problem Statement

Write a C program that prompts the user for the number of rows n and prints a right-angled triangle containing sequential prime numbers. Row 1 contains 1 prime number, Row 2 contains 2, Row 3 contains 3, and so on.

Pattern Analysis & Logic

• Rows (Outer Loop): i runs from 1 to n.

• Columns (Inner Loop): j runs from 1 to i, dictating how many prime numbers to display in the current row.

• Primality Check: A positive integer greater than 1 is prime if it has no positive divisors other than 1 and itself. We maintain a global candidate integer starting at 2 and increment it until we find the next prime value to print.

Step-by-Step Algorithm

1. Read the total number of rows n from the user.

2. Initialize a candidate number variable num = 2.

3. Execute an outer loop i from 1 to n.

4. Execute an inner loop j from 1 to i.

5. Within the inner loop, continuously test num using a primality check algorithm:

   • If num is prime, print num followed by a space, increment num, and move to the next column j.

   • If num is not prime, increment num and recheck until a valid prime is found.

6. Print a newline character (\n) after completing each row.

Code Implementation

#include <stdio.h>

#include <stdbool.h>

// Helper function to check if a number is prime
bool isPrime(int num) {
    if (num <= 1) return false;
    for (int k = 2; k * k <= num; k++) {
        if (num % k == 0) return false;
    }
    return true;
}

int main() {
    int n;

    // Prompt user for input
    printf("Enter the number of rows: ");
    if (scanf("%d", &n) != 1 || n <= 0) {
        printf("Please enter a valid positive integer.\n");
        return 1;
    }

    int currentNum = 2;

    // Outer loop for rows
    for (int i = 1; i <= n; i++) {
        // Inner loop for columns in row 'i'
        for (int j = 1; j <= i; j++) {
            // Find the next prime number
            while (!isPrime(currentNum)) {
                currentNum++;
            }
            // Print the valid prime number
            printf("%d ", currentNum);
            currentNum++;
        }
        // Move to the next line after completing the row
        printf("\n");
    }

    return 0;
}

Line-by-Line Code Breakdown

• bool isPrime(int num): A helper function that returns true if num is prime and false otherwise, optimizing checks up to sqrt{num}.

• if (scanf("%d", &n) != 1 || n <= 0): Performs strict input validation to guard against non-numeric or non-positive input values.

• int currentNum = 2;: Tracks the continuous sequence of integers, starting from the first prime number 2.

• while (!isPrime(currentNum)) { currentNum++; }: Skips non-prime numbers until the next prime integer is found.

• printf("%d ", currentNum); currentNum++;: Prints the identified prime number and increments the candidate tracker for subsequent iterations.

• printf("\n");: Terminates the current row line.

Compiling & Execution

Sample Run

Enter the number of rows: 5

2 
3 5 
7 11 13 
17 19 23 29 
31 37 41 43 47 

Variations & Enhancements

• Inverted Prime Triangle: Reverse the outer loop (for (int i = n; i >= 1; i--)) to print the largest row of prime numbers at the top.

• Conditional Primality Filtering: Print numbers from a standard counter, but display non-prime positions as symbols (e.g., *).

• Centered Pyramid: Add space-printing logic before the inner number loop to convert the right-angled triangle into a centered pyramid.

Common Mistakes & Troubleshooting

• Forgetting to Increment currentNum After Printing: If currentNum is not incremented after printing, the while loop will repeatedly find and print the exact same prime number.

• Unoptimized Primality Checks: Testing factors up to num - 1 rather than $\sqrt{\text{num}}$ significantly degrades performance for larger row counts.

• Treating 1 as Prime: Ensure your prime validation logic explicitly excludes 1, as 1 is neither prime nor composite.

Complexity Analysis

• Time Complexity: {O}(k \sqrt{m})$, where k is the total count of printed numbers (n(n+1)/2) and m is the value of the largest prime printed.

• Space Complexity: {O}(1) — operates in constant auxiliary space.

Combining algorithmic checks like primality testing with nested loops provides a solid foundation for mastering dynamic matrix operations.

Try modifying the code to create an Inverted Prime Triangle! Post your solution in the comments section below.

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…till the next post, bye-bye & take care