Prime Number Checker
Check if a number is prime and obtain its factorization into prime factors. Free online.
Free · No sign-up · Runs in your browser · Last reviewed November 2026
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What is a prime number and how do you check one?
A prime number is a whole number greater than 1 that has exactly two divisors: 1 and itself. 2, 3, 5, 7 and 11 are prime; 4, 6, 8, 9 and 10 are not, because they can be divided by other numbers. This prime number checker tells you instantly whether a number is prime and, if it is not, shows its prime factorization (for example 84 = 2 × 2 × 3 × 7).
How to check if a number is prime
- If the number is less than 2, it is not prime.
- If it is 2 or 3, it is prime. If it is even or a multiple of 3, it is not.
- Try dividing by every number up to its square root. If none divides it exactly, it is prime. For 97, the square root is about 9.8, so you only test 2, 3, 5 and 7: none divides 97, so it is prime.
Divisibility rules that save time
| Divisible by | Rule | Example |
|---|---|---|
| 2 | The last digit is even | 128 |
| 3 | The digit sum is divisible by 3 | 123 (1+2+3 = 6) |
| 5 | The last digit is 0 or 5 | 145 |
| 7 | Double the last digit and subtract it from the rest; repeat | 343 → 34 − 6 = 28 ✓ |
| 11 | Alternating digit sum is 0 or a multiple of 11 | 121 (1 − 2 + 1 = 0) |
The 25 prime numbers below 100
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.
Things worth knowing
- 2 is the only even prime. Every other even number is divisible by 2.
- 1 is not prime because it has only one divisor.
- Every whole number above 1 is either prime or a product of primes in exactly one way (the fundamental theorem of arithmetic). That is why prime factorization is unique.
- There are infinitely many primes, a fact proved by Euclid more than 2,000 years ago.
- Large primes protect online communication: encryption methods such as RSA depend on how hard it is to factor the product of two very large primes.
Related tools: GCF and LCM calculator, ratio calculator and random number generator.
How to use the Prime Number Checker
- Type any whole number from 2 up to 999,999,999,999,999 in the box.
- The result appears instantly, or press “Find out”: it tells you whether the number is prime.
- Read its prime factorization, its divisors (for numbers up to 1,000,000) and the previous and next prime.
List of prime numbers from 1 to 1,000
There are exactly 168 prime numbers below 1,000. The first 25 (every prime up to 100) are: 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. 2 is the only even prime; every other even number is divisible by 2.
Show all primes by hundred
0–99: 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
100–199: 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199
200–299: 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293
300–399: 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397
400–499: 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499
500–599: 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599
600–699: 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691
700–799: 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797
800–899: 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887
900–999: 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997
How many primes are there?
| Up to | Number of primes |
|---|---|
| 10 | 4 |
| 100 | 25 |
| 1,000 | 168 |
| 10,000 | 1,229 |
| 100,000 | 9,592 |
| 1,000,000 | 78,498 |
Numbers that look prime but are not
Some odd numbers pass the quick tests for 2, 3 and 5 and still are not prime. Common examples: 91 = 7 × 13, 119 = 7 × 17, 133 = 7 × 19, 143 = 11 × 13, 161 = 7 × 23, 169 = 13 × 13 and 187 = 11 × 17. So is 91 a prime number? No, it is 7 × 13. Type any of them into the checker above to see the factors.
Prime number FAQ
How do I know if a number is prime?
Check that no whole number from 2 up to its square root divides it exactly. If none does, it is prime. 97 is prime; 91 is not, because 91 = 7 × 13.
Is 1 a prime number?
No. A prime has exactly two divisors, and 1 has only one.
Is 2 a prime number?
Yes, and it is the only even prime number.
What are the first prime numbers?
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47. There are 25 primes below 100.
What is prime factorization?
Writing a number as a product of primes. 84 = 2 × 2 × 3 × 7, and every number has exactly one such factorization.
Why are prime numbers important?
They are the building blocks of all whole numbers and are essential in cryptography, which keeps online payments and messages secure.