Prime Number Checker
A prime number is divisible only by 1 and itself. First primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29. To check primality, test divisibility by primes up to √n. There are 25 primes below 100.
Check if a number is prime. See prime factorization, all factors, and find next/previous primes.
Enter a Number
What is a Prime Number?
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. The first few primes are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29...
How to Use
- 1
Enter a number
Input the number you want to check
- 2
Check primality
Click Check to determine if the number is prime
- 3
View factors
If not prime, see the prime factorization
Frequently Asked Questions
- What is a prime number?
- A prime number is a natural number greater than 1 that is only divisible by 1 and itself. Examples: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31... The number 2 is the only even prime. 1 is not considered prime.
- How do I check if a number is prime?
- Check divisibility by all primes up to √n. For 97: √97 ≈ 9.8, check 2, 3, 5, 7. 97 is odd (not ÷2), 9+7=16 (not ÷3), doesn't end in 0/5 (not ÷5), 97/7=13.8 (not ÷7). No divisors found, so 97 is prime.
- What are the first 100 prime numbers?
- First 25: 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. There are exactly 25 primes below 100. The 100th prime is 541.
- Why are prime numbers important?
- Primes are fundamental in mathematics and cryptography. RSA encryption relies on difficulty of factoring large products of primes. Primes have no pattern, making them useful for hashing and random-seeming sequences. They are the "atoms" of multiplication.
- What is the largest known prime number?
- The largest known primes are Mersenne primes (2^p - 1). As of 2024, the largest is 2^82,589,933 - 1, discovered in 2018, with 24,862,048 digits. Finding new large primes continues via distributed computing projects like GIMPS.
- Is 1 a prime number?
- No, 1 is not a prime number. By definition, prime numbers must be greater than 1 and have exactly two distinct factors: 1 and themselves. The number 1 has only one factor (itself), so it does not meet the definition. The smallest prime number is 2.
- What are composite numbers?
- A composite number is a positive integer greater than 1 that has at least one factor other than 1 and itself. Examples: 4 (factors: 1,2,4), 6 (factors: 1,2,3,6), 9 (factors: 1,3,9). Every composite number can be expressed as a product of prime factors (fundamental theorem of arithmetic).
- What are twin primes?
- Twin primes are pairs of primes that differ by 2. Examples: (3,5), (5,7), (11,13), (17,19), (29,31), (41,43), (59,61). It is conjectured (but unproven) that there are infinitely many twin prime pairs. The largest known twin prime pair has over 388,000 digits each.
- How many prime numbers are there below 1000?
- There are 168 prime numbers below 1000. Key milestones: 4 primes below 10 (2,3,5,7), 25 primes below 100, 168 primes below 1000, 1,229 primes below 10,000. The prime counting function π(n) gives the count of primes ≤ n.