Prime Number Checker

Prime Number Checker tells you whether a whole number is prime and, if it is not, gives the smallest number that divides it. It checks for factors only up to the square root, which is sufficient: any factor larger than the square root pairs with one smaller than it, so if none exists below, none exists above.

That shortcut is what makes checking large numbers quick. For 97 it means testing divisibility up to 9 rather than up to 96, and the saving grows with the number. The working section states the bound it used so you can see why the answer is conclusive rather than a guess.

One and zero are neither prime nor composite, and the calculator says so rather than giving a misleading yes or no. A prime has exactly two distinct divisors, one and itself; one has only a single divisor, which is why excluding it is a definition rather than an oversight.

The page shows its working, not just its answer. Where there is a formula it is printed with your own numbers substituted in, so you can check the result rather than take it on trust -- which is the difference between a calculator you can use for something that matters and one you cannot.

Everything runs inside your browser. What you type is never uploaded, never logged and never stored, and the calculator keeps working if your connection drops after the page has loaded.

• Shows prime, smallest factor, number of divisors, previous prime and next prime together, so you are not running it twice
• A results table you can read across
• Prints the formula with your own figures substituted in
• Updates as you type, with no button to press and no page reload
• Copy the result in one click
• Free, no sign-up, and it runs entirely in your browser

The prime number checker is used by writers, developers, students, marketers and anyone else who needs the job done once without installing software. Common cases include:

• Checking a number in a homework problem
• Finding the next prime above a given value
• Getting the smallest factor of a stubborn number
• Looking at the gaps between consecutive primes