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Learn to build a prime number checker in JavaScript with trial division, Sieve of Eratosthenes, prime factorization, and range prime finder visualization.
What You'll Learn
- How to implement the trial division algorithm for primality testing
- Why we only need to check divisors up to √n (and why this is efficient)
- How to implement the Sieve of Eratosthenes to find all primes in a range
- How to display prime factorization of composite numbers
- How to visualize a grid of primes up to 100
Project Overview
A prime number checker tests whether an input number is prime, explains why (showing divisibility), and optionally generates all primes in a range. It's an excellent algorithm project that teaches loop optimization.
Component Structure
How It Works — Flow Diagram
Step-by-Step Build
Step 1 — HTML Structure
html example
<div class="prime-checker">
<h1>Prime Number Checker</h1>
<div class="input-row">
<input type="number" id="numInput" placeholder="Enter a number (≥ 2)" min="2" step="1">
<button id="checkBtn">Check</button>
</div>
<div id="result" class="result hidden"></div>
<div id="factBox" class="fact-box hidden"></div>
<div class="sieve-section">
<h2>Primes up to 100</h2>
<div id="primeGrid" class="prime-grid"></div>
</div>
</div>Step 2 — isPrime (Trial Division)
js example
function isPrime(n) {
n = Math.floor(n);
if (n < 2) return { prime: false, reason: "Numbers less than 2 are not prime" };
if (n === 2) return { prime: true, reason: "2 is the only even prime" };
if (n % 2 === 0) return { prime: false, reason: `${n} is even — divisible by 2` };
const limit = Math.sqrt(n);
for (let i = 3; i <= limit; i += 2) {
if (n % i === 0) {
return { prime: false, reason: `Divisible by ${i} (${n} ÷ ${i} = ${n / i})` };
}
}
return { prime: true, reason: `No divisors found between 2 and √${n} ≈ ${limit.toFixed(2)}` };
}Step 3 — Prime Factorization
Example
function factorize(n) {
const factors = {};
let d = 2;
while (d * d <= n) {
while (n % d === 0) {
factors[d] = (factors[d] || 0) + 1;
n = Math.floor(n / d);
}
d++;
}
if (n > 1) factors[n] = (factors[n] || 0) + 1;
// Format: 84 = 2² × 3 × 7
const formatted = Object.entries(factors)
.map(([base, exp]) => exp > 1 ? `${base}${toSuperscript(exp)}` : base)
.join(" × ");
return formatted;
}
function toSuperscript(n) {
const map = "⁰¹²³⁴⁵⁶⁷⁸⁹";
return String(n).split("").map(d => map[d]).join("");
}
Step 4 — Render Result
Example
function check() {
const raw = document.getElementById("numInput").value;
const n = parseInt(raw, 10);
const resultEl = document.getElementById("result");
const factBox = document.getElementById("factBox");
if (!raw || isNaN(n) || n < 2 || !Number.isInteger(Number(raw))) {
resultEl.textContent = "⚠️ Please enter an integer ≥ 2";
resultEl.className = "result warning";
resultEl.classList.remove("hidden");
factBox.classList.add("hidden");
return;
}
const { prime, reason } = isPrime(n);
resultEl.classList.remove("hidden");
factBox.classList.remove("hidden");
if (prime) {
resultEl.textContent = `✅ ${n} is a PRIME number`;
resultEl.className = "result success";
factBox.textContent = reason;
} else {
resultEl.textContent = `❌ ${n} is NOT a prime number`;
resultEl.className = "result failure";
const factors = factorize(n);
factBox.innerHTML = `
${reason}<br>
Factorization: <strong>${n} = ${factors}</strong>
`;
}
highlightInGrid(n);
}
Step 5 — Sieve of Eratosthenes (Grid up to 100)
Example
function sieve(limit) {
const isP = new Array(limit + 1).fill(true);
isP[0] = isP[1] = false;
for (let i = 2; i * i <= limit; i++) {
if (isP[i]) {
for (let j = i * i; j <= limit; j += i) isP[j] = false;
}
}
return isP;
}
function buildPrimeGrid() {
const LIMIT = 100;
const isP = sieve(LIMIT);
const grid = document.getElementById("primeGrid");
grid.innerHTML = Array.from({ length: LIMIT - 1 }, (_, i) => {
const n = i + 2;
return `<span class="grid-cell ${isP[n] ? "prime" : "composite"}" data-n="${n}">${n}</span>`;
}).join("");
}
Step 6 — Highlight Checked Number in Grid
Example
function highlightInGrid(n) {
document.querySelectorAll(".grid-cell").forEach(cell => {
cell.classList.toggle("highlighted", Number(cell.dataset.n) === n);
});
}
Step 7 — Wire Events & Initialize
Example
document.getElementById("checkBtn").addEventListener("click", check);
document.getElementById("numInput").addEventListener("keydown", (e) => {
if (e.key === "Enter") check();
});
buildPrimeGrid();
Console Output
Output
isPrime(2) → { prime: true, reason: "2 is the only even prime" }
isPrime(97) → checks 3,5,7,9 up to √97≈9.85 → no divisors → { prime: true }
isPrime(84) → 84 % 2 === 0 → { prime: false, reason: "Divisible by 2 (84 ÷ 2 = 42)" }
isPrime(1) → { prime: false, reason: "Numbers less than 2 are not prime" }
isPrime(49) → 49 % 7 === 0 → { prime: false, reason: "Divisible by 7 (49 ÷ 7 = 7)" }
factorize(84) → 2² × 3 × 7
factorize(360) → 2³ × 3² × 5Edge Cases to Handle
| Input | Expected |
|---|---|
| 1 | Not prime (by definition) |
| 2 | Prime (only even prime) |
| 0 or negative | Warning |
| Decimal (3.5) | Warning — must be integer |
| Very large number (1e9) | Trial division still fast up to ~1M; warn for huge numbers |
Challenge Yourself
- Twin primes — find all pairs of primes that differ by 2 (e.g., 11 & 13)
- Next prime — show the next prime after the entered number
- Goldbach's conjecture — express any even number > 2 as the sum of two primes
- Performance benchmark — time
isPrime(n)for n = 10⁶, 10⁷, 10⁸ - Miller-Rabin test — implement the probabilistic primality test for huge numbers
Best Practices
- Only loop up to √n — checking beyond is redundant
- Skip even numbers in the loop (
i += 2after checking 2 separately) — halves the work - Always validate input: check for
isNaN,< 2, and!Number.isInteger Number.isInteger(Number(raw))catches decimals like3.5- The Sieve is great for ranges — trial division is great for individual numbers
Continue the lesson path
Study next in this module
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