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This prime number calculator will find if a number is prime or composite. Check for primality of any whole number up to 500 digits long.

What is a Prime Number?

A prime number is a whole number greater than 1 that is only divisible by 1 and itself. In other words, a prime number has only two factors, 1 and itself. A number that is not a prime is a composite number which means it has more than two factors.

How the Prime Checker Works

This prime number calculator checks whether a number is prime or composite using prime factorization. This means we divide your number by prime numbers until we find all its factors. If your number is not divisible by any prime number or composite number, your number is prime!

If your number is a composite number and less than 15 digits long, the calculator lists all factors of the composite number.

You can also use the CalculatorSoup® Factoring Calculator to find all factors of a number, or to decompose a number into prime or exponential form.

Checking Primality of Large Numbers

When testing numbers that are more than 15 digits long -- more than 1 quadrillion, 1,000,000,000,000,000 -- this calculator uses the Miller–Rabin primality test. This algorithm returns either "yes" or "no" or "probably" prime when checking a number.

A probable prime is a number that is likely prime given certain attributes common to all prime numbers. The Miller-Rabin primality test is used when a number is so large that it takes extensive computing power to conclude absolutely whether a number is prime.

Check for Primes

There are many ways you can check whether a number is prime on your own. Some require memorization and others need only a few steps of math.

Is 1 a Prime Number?

Since the only factor of 1 is 1, that means 1 is not a prime number. 1 is not composite either because it has fewer than two positive factors.

Prime Numbers 1-100

There are 25 prime numbers between 1 and 100. We list them here so you can reference them or even memorize them:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

You can also reference the first 100 prime numbers listed in the table below. We include the first 109 primes to complete the last row in the table. Notice that if you pause your cursor over a cell you'll see a note "Prime[xx]". The xx refers to the n^th prime number. For example, Prime[13] = 41 because 41 is the 13th prime number.

Prime Numbers 1-1000

There are 168 prime numbers between 1 and 1000. We list them here so you can reference them or memorize them if you feel like a challenge!

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997

CalculatorSoup® proudly provides a list of the first 1000 prime numbers for your reference. See our 1000 Prime Numbers Table and bookmark it for easy access.

The Square Root Method to Check for Primality

You can do a little math to figure out whether a number is prime. As an alternative to Prime Factorization where you find all prime factors of a number, you can use the square root method. The steps for the squre root method are:

1. Find the square root of the number in question
2. List all of the primes less than the square root
3. Divide your number by each of the primes in your list
4. If your suspected prime is not divisible by any of the primes in your list, that number is also prime

Note that you if your square root is a whole number, the number you're checking is not prime because it has a pair of factors that are not 1 and the number itself.

Also, you don't have to check numbers larger than the square root. This is because if you find any factor less than the square root, that number will have a factor pair match that is greater than the square root.

Example Using Square Roots to Check for Primality

You are wondering whether the number 417 is prime. It's not an even number, so it's not divisible by 2 and another factor. Is it possible that 417 is a prime number? Use the square root method to check.

1. Find the square root of 417: √417 = 20.42
2. List all of the primes less than 20.42: 2, 3, 5, 7, 11, 13, 17, 19
3. Divide 417 by each of the primes in your list
• 417 ÷ 2 = 208.5
• 417 ÷ 3 = 139
• 417 ÷ 5 = 83.4
• 417 ÷ 7 = 59.571
• 417 ÷ 9 = 46.333
• 417 ÷ 11 = 37.909
• 417 ÷ 13 = 32.077
• 417 ÷ 17 = 24.529
• 417 ÷ 19 = 21.947
4. If your suspected prime is not divisible by any of the primes in your list, that number is also prime. Since 417 is divisible by 3 it has a factor pair of 3, 139. So your number is not prime.

Why are Prime Numbers Important?

Prime numbers are important as a basic math concept. You can think of them as the "building blocks" of all other whole numbers. Just as atoms are the building blocks of physical matter, prime numbers make up all other whole numbers through multiplication.

Primes are particularly important in computer security and encryption. It's relatively easy to multiply two large numbers together to get an even larger number. But it would take a lot of time to find the factors of a very large number. This is what helps keep encrypted data safe. Encryption uses the easy multiplication method to lock sensitive data, but a hacker would have a hard time doing the factoring to unlock it.

Examples of Prime Numbers

Is 2 a prime number? Yes, 2 is a prime number because it only has two factors, 1 and 2.

Is 17 a prime number? Yes, 17 is a prime number because it only has two factors, 1 and 17.

Is 51 a prime number? No, 51 is NOT a prime number because it has more than two factors. 51 is a composite number and can be factored by the numbers: 1, 3, 17, 51.