Checking Whether a Number Is Prime

In this lesson you will learn the algorithm for testing whether a number is prime and understand how to make it efficient. This is for anyone searching for "Ruby prime number check".

To decide whether a number is prime (divisible only by 1 and itself), check whether it divides evenly by anything from 2 up to its square root. If nothing divides it, it is prime.

The sample code loops over (2..Math.sqrt(n)), which effectively covers only "up to the square root". Computing the square root with Math.sqrt(n) and looping over that range is the key idea.

A common stumbling block for beginners is understanding why the square root is enough. Any pair of numbers that multiply to give the value always has one member at or below the square root and the other at or above it, so checking up to the square root covers every case.

This is an important mathematical property that also underpins cryptography, and good practice at designing an efficient test. There is a more advanced technique, the Sieve of Eratosthenes, for finding many primes efficiently at once.

📖 Reference code

def prime?(n)
  return false if n < 2
  (2..Math.sqrt(n)).each do |i|
    return false if n % i == 0
  end
  true
end

puts prime?(17)
puts prime?(18)

✍️ Your code

Type your code, then press "Run"

🧪 This site can't compile or run Ruby directly, so it checks on the spot whether what you typed matches the reference code (scoring happens entirely in your browser — nothing is sent anywhere).