Page 43 - Revised Maths Wisdom Class - 6

Prime Time 41

ILLUSTRATIONS

Example 1: Write all the prime numbers and composite numbers less than 30.
Solution: Prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29.

Composite numbers are 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 26, 28.
Example 2: Using Sieve of Eratosthenes, find:
(a) Five consecutive composite numbers. (b) All twin primes from 1 to 100.

Solution: (a) The five consecutive composite numbers are 62, 63, 64, 65 & 66 and 74, 75, 76, 77 and 78.
(b) All twin primes from 1 to 100 are:
(3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), (59, 61) and (71, 73).

Example 3: Express the following as sum of twin primes:
(a) 60 (b) 144

Solution: (a) 60 = 29 + 31 (b) 144 = 71 + 73

Remember!er!
Rememb
› Divide the given number by 2. Add 1 and subtract 1 to get the set of twin primes.

Example 4: Write the smallest even prime number and the smallest odd composite number.

Solution: 2 is the smallest even prime number.
9 is the smallest odd composite number.

Exercise 3B
Exercise 3B
1. Write all prime numbers and composite numbers between 25 and 60.
2. How many prime numbers up to 100 have 3 at their ones place?

3. Express the following as a sum of two odd primes:
(a) 72 (b) 66 (c) 40 (d) 52
4. Express the following as sum of twin primes:

(a) 84 (b) 120
5. Write any four examples of co-primes.
6. Write the seven consecutive composite numbers less than 100.
7. A two digit number has 5 at its ones place. Will it be prime? Justify your answer.

8. Write five pairs of odd primes less than 20 whose sum is divisible by 4.
9. Express the following as sum of three odd primes:
(a) 63 (b) 95 (c) 49

10. State whether the following statements are correct or not. Justify your answer:
(a) Every prime number is odd. (b) Every whole number is either prime or composite.
(c) The product of prime numbers cannot be a prime number.