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Co-prime and Twin Prime

Let’s take a pair of composite numbers, say 8 and 15. Try to find out its factors.

8 15

1 2 4 8 1 3 5 15

Do you find any factor other than 1 common? Obviously, no.
Two numbers are said to be co-prime to each other if there Knowledge Desk
is no other factor except 1 is common between them. Here, Prime Triplet
8 and 15 is a pair of co-prime. Some more such pairs are: A set of three consecutive prime
(13, 14), (28, 57), (46, 67) etc. numbers that have a difference of
2 are called prime triplets. (3, 5, 7)
Pairs of primes with a difference of 2 are called twin primes. is the only prime triplet.
For example: (3, 5), (11, 13), (17,19), etc.

Practice Time 5C

1. State whether the following statements are True (T) or False (F).

(a) If an even number is divided by 2, the quotient is always odd.

(b) All prime numbers except 2 are odd.

(c) 2 is the only even prime number.
(d) All even numbers are composite numbers.

(e) The sum of two prime numbers can never be a prime number.

(f) There is no prime number whose unit digit is 4.
(g) A product of primes can also be prime.

(h) There are infinitely many prime numbers between 1 and 10000.

2. How many prime numbers are there between 50 and 100? List them.

3. State whether the following numbers are pairs of co-primes.
(a) 9, 16 (b) 5, 17 (c) 10, 25 (d) 13, 21

4. Write down all the pairs of twin primes from 1 to 100.

5. Write three pairs of prime numbers less than 20 whose difference is a multiple of 4.

6. Can you express a prime number as the (a) sum of odd primes (b) product of two primes?
7. Find the prime numbers between 101 and 200.

8. How many three-digit prime numbers can you make using each of the digits 2, 3 and 5 once?

149 Prime Time