What is a prime number?

A prime number is a whole number greater than 1 whose only divisors are 1 and itself. The first few are 2, 3, 5, 7, 11 and 13. Numbers greater than 1 that are not prime are called composite.

How many primes are there below 1,000?

There are exactly 168 prime numbers from 2 to 997. The density of primes thins out as numbers grow, a pattern described by the prime number theorem.

No. By definition a prime must have exactly two distinct divisors, 1 and itself. The number 1 has only one divisor, so it is neither prime nor composite. The number 2 is the smallest prime and the only even one.

How does the checker decide if a number is prime?

It uses trial division: it tests divisibility by 2, then by odd numbers up to the square root of the input. If any divides evenly the number is composite and the smallest such factor is shown; otherwise it is prime. Checking up to the square root is enough because a larger factor must pair with a smaller one.

Is this data sent anywhere?

No. The table and the primality check run entirely in your browser. Nothing is uploaded, logged or stored.

Prime Numbers Reference Table

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Prime numbers up to 1,000

A prime number is a whole number greater than 1 divisible only by 1 and itself. This reference lists all 168 primes from 2 to 997, each with its index in the sequence, and includes a checker that tests any number you type for primality.

How it works

The checker uses trial division. To decide whether n is prime it tests divisibility by 2, then by each odd number 3, 5, 7, … up to √n. If any divides n evenly, n is composite and the smallest such divisor is its smallest prime factor. If none do, n is prime. Testing only up to the square root is sufficient: if n = a × b with a ≤ b, then a ≤ √n, so a factor larger than the root always pairs with a smaller one already checked.

Tips and example

The only even prime is 2; every other even number is divisible by 2.
A number ending in 0 or 5 (above 5) is divisible by 5, never prime.
There are 168 primes below 1000, 25 of them below 100.
Twin primes — pairs differing by 2, like (11, 13) or (17, 19) — appear throughout the list.