Prime Number Checker
Check if a number is prime, see its factors if composite, and find the next 10 prime numbers with list primes up to N
Is 17 prime?
✓ Yes
Next 10 primes after 17
19, 23, 29, 31, 37, 41, 43, 47, 53, 59
What's a Prime Number?
A prime is a number greater than 1 that has only two divisors: 1 and itself. So 7 is prime (only 1 and 7 divide it). 8 is not (1, 2, 4, 8 divide it). The first primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29... 2 is the only even prime; all other primes are odd.
Primes are foundational in cryptography, number theory, and computer science. RSA encryption (used for HTTPS, banking) relies on the difficulty of factoring large numbers into their prime components. The largest known prime as of 2024: 2^82,589,933 - 1, which has 24.8 million digits. New primes are discovered occasionally by distributed computing projects (GIMPS).
First Primes by Range
| Range | Primes |
|---|---|
| 1-10 | 2, 3, 5, 7 |
| 11-20 | 11, 13, 17, 19 |
| 21-30 | 23, 29 |
| 31-50 | 31, 37, 41, 43, 47 |
| 51-100 | 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 |
| 100s | 25 primes (101-199) |
| 1000s | 143 primes |
| 100000s | 10,000+ primes |
Frequently Asked Questions
How do I quickly check if a number is prime?
For small numbers, divide by primes up to √n. So for 91: check 2, 3, 5, 7. 91 ÷ 7 = 13. So 91 = 7 × 13, NOT prime. For numbers under 100, you only need to check division by 2, 3, 5, 7 (primes up to √100 = 10).
Why is 1 not prime?
By definition - primes need exactly two divisors (1 and themselves). 1 has only one divisor (itself). The exclusion makes prime factorisation work cleanly: every number has a unique prime factorisation if 1 is excluded. Including 1 would break that uniqueness.