Prime Numbers
Prime vs composite; 2 as only even prime; twin primes intro.
Prime Numbers
Prime and Composite Numbers
What you'll learn
- A prime has exactly two factors: 1 and itself.
- A composite has more than two factors.
- Know that 2 is the only even prime; spot twin primes (intro).
Key concepts
Level 1 — Prime vs composite
| Type | Factors | Examples |
|---|---|---|
| Prime | Exactly 2 (1 and itself) | 2, 3, 5, 7, 11, 13 |
| Composite | More than 2 | 4, 6, 8, 9, 10, 12 |
| Special | 1 has only one factor | 1 is neither prime nor composite |
Level 2 — Testing small numbers
Is 17 prime? Check division by 2, 3, 4 — none divide exactly → prime.
Is 21 prime? 21 = 3 × 7 → composite.
Level 3 — 2 is special
2 is the only even prime. All other even numbers ≥ 4 are composite (divisible by 2).
Level 4 — Twin primes (intro)
Pairs differing by 2: (3, 5), (5, 7), (11, 13), (17, 19).
Indian context: Sieve of Eratosthenes — ancient method; Indian mathematicians studied number patterns for centuries.
NCERT anchor: Math-Magic 4, Ch 14 — Play with Patterns; Ch 11 — Tables and Shares (rectangular arrays)
Worked example
Is 29 prime or composite?
Step 1 — Try 2: 29 is odd → not divisible by 2.
Step 2 — Try 3: 2+9=11, not divisible by 3.
Step 3 — Try 5: doesn't end in 0 or 5.
Step 4 — 5²=25 < 29; 7²=49 > 29 — test up to 5 only.
Answer: **29 is prime**
List prime numbers between 10 and 25
Step 1 — Check 11 ✓, 12 ✗, 13 ✓, 14 ✗, 15 ✗, 16 ✗, 17 ✓.
Step 2 — 18–19: 19 ✓; 20–23: 23 ✓.
Answer: **11, 13, 17, 19, 23**
Common mistakes
| Mistake | Why it happens | Fix |
|---|---|---|
| 1 is prime | Thinking 'only divisible by 1' | 1 has one factor — neither prime nor composite |
| All odd numbers are prime | 9 = 3×3, 15 = 3×5 | Check factors — 9 is composite |
| 2 is composite because it's even | All evens divisible by 2 | 2 has only factors 1 and 2 → prime |
| Twin primes must be consecutive | Confusing with consecutive numbers | Twin primes differ by 2, not 1 (e.g. 11 and 13) |
Quick check
- Is 1 prime? (no)
- Smallest prime number? (2)
- Is 39 prime? (no — 3×13)
- Stretch: Find the only pair of twin primes between 30 and 50. (41 and 43)
Revision tip: Cross out composites on a 1–50 grid using the Sieve method — primes remain unmarked.
Open the Practice tab for graded questions on Prime and Composite Numbers.
Key Takeaways (TL;DR)
- What you'll learn
- Key concepts
- Worked example
- Common mistakes
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