What Is Prime Number?
A prime number is a whole number greater than 1 that has exactly two positive divisors: 1 and itself.
Examples of Prime Number
1
22
33
54
75
116
13Formula and Key Points
Formula / rule
A prime p has exactly two positive factors: 1 and p.
- 2 is the only even prime number.
- 1 is not prime.
- A composite number has more than two positive divisors.
- Every integer greater than 1 can be built from prime factors.
Why This Matters in Computer Science
Used in cryptography, hashing, coding theory, security protocols and efficient integer algorithms.
Worked Example
Problem
Is 29 a prime number?
- Check divisibility by primes up to √29, which is a little over 5.
- 29 is not divisible by 2.
- 29 is not divisible by 3.
- 29 is not divisible by 5.
- Therefore 29 has no positive divisors other than 1 and 29.
✓
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Final AnswerYes, 29 is prime.
Prime vs Composite Number
| Feature | Prime | Composite |
|---|---|---|
| Positive divisors | Exactly 2 | More than 2 |
| Example | 13 | 12 |
| Smallest example | 2 | 4 |
Related Math Terms
Prime Number: Frequently Asked Questions
Is 1 a prime number?
No. A prime must have exactly two positive divisors, but 1 has only one.
What is the smallest prime number?
2.
Is 2 prime?
Yes, and it is the only even prime number.