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. In other words, a prime number can only be divided evenly by 1 and the number itself.
First 25 Prime Numbers
How to Check if a Number is Prime
Numbers less than 2 are not prime
By definition, prime numbers must be greater than 1.
Check 2 separately
2 is the only even prime. All other even numbers are not prime.
Test divisibility up to √n
If no number from 2 to √n divides n evenly, then n is prime.
Example: Is 29 prime?
Prime vs Composite Numbers
Prime Numbers
Exactly two factors: 1 and itself
Examples: 2, 3, 5, 7, 11, 13, 17...
Composite Numbers
More than two factors
Examples: 4, 6, 8, 9, 10, 12, 14...
Special Cases
Is 1 Prime?
No. 1 has only one factor (itself), not two. It is neither prime nor composite.
Is 0 Prime?
No. 0 is divisible by every number except itself, and prime numbers must be greater than 1.
Is 2 Prime?
Yes! 2 is the smallest and only even prime number. Its only factors are 1 and 2.
Why Prime Numbers Matter
Cryptography
RSA encryption relies on the difficulty of factoring large numbers into primes. This secures online banking and communications.
Fundamental Theorem of Arithmetic
Every integer greater than 1 can be uniquely expressed as a product of prime numbers.
Finding GCD & LCM
Prime factorization is the foundation for calculating the Greatest Common Divisor and Least Common Multiple.
Mathematics & Research
Prime numbers are central to number theory and have fascinated mathematicians for thousands of years.
Quick Divisibility Tips
- Divisible by 2: Last digit is even (0, 2, 4, 6, 8)
- Divisible by 3: Sum of digits is divisible by 3
- Divisible by 5: Last digit is 0 or 5
- Divisible by 11: Alternating sum of digits is divisible by 11