Check if Number is Prime in DSA Go - Build from Scratch

Check if Number is Prime

📖 Scenario: You are helping a friend who wants to check if a number is prime. A prime number is a number greater than 1 that has no divisors other than 1 and itself.Imagine you have a list of numbers and you want to find out which ones are prime.

🎯 Goal: You will write a Go program that checks if a given number is prime by testing divisibility from 2 up to the number minus one.This will help your friend quickly know if a number is prime or not.

📋 What You'll Learn

Create a variable called number with the value 29

Create a variable called isPrime and set it to true

Use a for loop with variable i from 2 to number - 1

Inside the loop, check if number is divisible by i

If divisible, set isPrime to false and break the loop

After the loop, print "Prime" if isPrime is true, else print "Not Prime"

💡 Why This Matters

🌍 Real World

Checking if a number is prime is useful in cryptography, coding challenges, and mathematical computations.

💼 Career

Understanding loops, conditionals, and boolean logic is essential for software development and algorithm design.

1

Create the number variable

Create a variable called number and set it to 29.

DSA Go

# Your code here

Hint

Use number := 29 to create the variable.

2

Create the isPrime variable

Create a variable called isPrime and set it to true after the number variable.

DSA Go

package main

func main() {
    number := 29
    // Your code here
}

Hint

Use isPrime := true to create the variable.

3

Check divisibility with a for loop

Use a for loop with variable i starting from 2 up to number - 1. Inside the loop, check if number % i == 0. If yes, set isPrime to false and use break to exit the loop.

DSA Go

package main

func main() {
    number := 29
    isPrime := true
    // Your code here
}

Hint

Use a for loop and inside it an if statement to check divisibility.

4

Print if the number is prime or not

After the loop, use if isPrime to print "Prime". Otherwise, print "Not Prime".

DSA Go

package main

import "fmt"

func main() {
    number := 29
    isPrime := true
    for i := 2; i < number; i++ {
        if number%i == 0 {
            isPrime = false
            break
        }
    }
    // Your code here
}

Hint

Use fmt.Println("Prime") or fmt.Println("Not Prime") based on isPrime.

Practice

1. What does it mean for a number to be prime?

easy

A. It has more than two divisors.

B. It is divisible by 2 only.

C. It is an even number greater than 2.

D. It has exactly two distinct positive divisors: 1 and itself.

Solution

1. Step 1: Understand the definition of prime number

   A prime number is a number greater than 1 that has no divisors other than 1 and itself.

2. Step 2: Compare options with definition

   It has exactly two distinct positive divisors: 1 and itself. matches this definition exactly, while others describe incorrect properties.

3. Final Answer:

   It has exactly two distinct positive divisors: 1 and itself. -> Option D

4. Quick Check:

   Prime number = two divisors only [OK]

Hint: Prime means only divisible by 1 and itself [OK]

Common Mistakes:

• Thinking even numbers are always prime
• Confusing prime with odd numbers
• Believing 1 is prime

2. Which of the following Go code snippets correctly checks if a number n is prime?

easy

A. for i := 2; i < n; i++ { if n%i == 0 { return false } } return true

B. for i := 2; i <= n; i++ { if n%i == 0 { return false } } return true

C. for i := 1; i < n; i++ { if n%i == 0 { return false } } return true

D. for i := 2; i < n/2; i++ { if n%i == 0 { return true } } return false

Solution

1. Step 1: Analyze loop range for prime check

   We check divisors from 2 up to but not including n to find if n is divisible by any number other than 1 and itself.

2. Step 2: Evaluate each option's correctness

   for i := 2; i < n; i++ { if n%i == 0 { return false } } return true correctly loops from 2 to n-1 and returns false if divisible. for i := 2; i <= n; i++ { if n%i == 0 { return false } } return true incorrectly includes n itself, always returning false. for i := 1; i < n; i++ { if n%i == 0 { return false } } return true starts from 1, which divides all numbers. for i := 2; i < n/2; i++ { if n%i == 0 { return true } } return false returns true on divisor found, which is wrong logic.

3. Final Answer:

   for i := 2; i < n; i++ { if n%i == 0 { return false } } return true -> Option A

4. Quick Check:

   Loop 2 to n-1 and check divisibility [OK]

Hint: Loop from 2 to n-1, return false if divisible [OK]

Common Mistakes:

• Checking divisibility including n itself
• Starting loop from 1 instead of 2
• Returning true when divisor found

3. What will be the output of this Go function call: isPrime(11)?

func isPrime(n int) bool {
 if n <= 1 {
  return false
 }
 for i := 2; i*i <= n; i++ {
  if n%i == 0 {
   return false
  }
 }
 return true
}

medium

A. true

B. false

C. runtime error

D. infinite loop

Solution

1. Step 1: Check input and loop condition

   Input n=11 is greater than 1, so function proceeds. Loop runs from i=2 while i*i <= 11 (i <= 3).

2. Step 2: Test divisibility inside loop

   Check i=2: 11%2 != 0; i=3: 11%3 != 0. No divisor found, loop ends.

3. Final Answer:

   true -> Option A

4. Quick Check:

   11 is prime, function returns true [OK]

Hint: Check divisors up to sqrt(n) for efficiency [OK]

Common Mistakes:

• Not handling n <= 1 correctly
• Looping beyond sqrt(n)
• Assuming 11 is not prime

4. Identify the bug in this Go function that checks if a number is prime:

func isPrime(n int) bool {
 if n <= 1 {
  return false
 }
 for i := 2; i < n/2; i++ {
  if n%i == 0 {
   return false
  }
 }
 return true
}

medium

A. Loop should run until i <= n, not i < n/2

B. Function should return true if n <= 1

C. Loop should run until i*i <= n for efficiency and correctness

D. The modulo operator % is used incorrectly

Solution

1. Step 1: Analyze loop range and condition

   The loop runs from 2 to less than n/2, which is inefficient and may miss divisors for small n.

2. Step 2: Suggest correct loop condition

   Looping until i*i <= n is both correct and efficient because any divisor larger than sqrt(n) pairs with a smaller divisor already checked.

3. Final Answer:

   Loop should run until i*i <= n for efficiency and correctness -> Option C

4. Quick Check:

   Use i*i <= n to check divisors [OK]

Hint: Check divisors up to sqrt(n) to fix bugs [OK]

Common Mistakes:

• Looping only to n/2 misses some divisors
• Returning true for n <= 1
• Misusing modulo operator

5. You want to find all prime numbers up to 20 using Go. Which approach is best to optimize performance?

hard

A. Check divisibility for each number up to n-1 without optimization

B. Check each number from 2 to 20 using a function that tests divisibility up to sqrt(n)

C. Use a loop from 2 to 20 and mark all numbers as prime without checks

D. Only check even numbers for primality since odd numbers are not prime

Solution

1. Step 1: Understand prime checking for multiple numbers

   Checking each number from 2 to 20 individually is necessary to find all primes.

2. Step 2: Optimize divisibility checks

   Testing divisibility only up to sqrt(n) for each number reduces unnecessary checks and improves performance.

3. Final Answer:

   Check each number from 2 to 20 using a function that tests divisibility up to sqrt(n) -> Option B

4. Quick Check:

   Use sqrt(n) limit for each number check [OK]

Hint: Test divisibility up to sqrt(n) for each number [OK]

Common Mistakes:

• Checking all numbers up to n-1 wastes time
• Ignoring odd numbers which can be prime
• Marking all numbers prime without checks