PLAYING WITH NUMBERS ( POST 3)

March 30, 2020

Good morning students !

Welcome to mathematics blog lesson.

Topic is -"Playing with numbers"

Today, by the end of the lesson you will be able to:

      1.      define Twin primes.

2.      Identify and give examples of twin primes.

What are Twin Primes?

Two prime numbers are called twin primes if there is present only one composite number between them. Or we can also say two prime numbers whose difference is two are called twin primes. For example, (3,5) are twin primes, since the difference between the two numbers 5 – 3 = 2. The alternative names, given to twin primes are prime twin or prime pair.

Properties of Twin Primes

• (2,3) are not considered as twin primes, since there is no composite number in between them and the difference between the two primes is not equal to 2.
• 5 is an only prime number which is available in two different pairs.
• The sum of each pair of Twin prime apart from (3,5) is divisible by 12.

First Few Pairs of Twin Primes

The first fifteen pairs of twin primes are as follows:

(3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), (59, 61), (71, 73), (101, 103), (107, 109), (137, 139),….

Let’s continue Ex-3.2 (page no. 53 & 54)

Q6: Express the following as the sum of two odd primes.

      a)      44

Explanation: According to the question,

▪ express the number as sum of two different numbers.

▪ those two different numbers should be odd and prime as well

Solution: 13 + 31 = 44 (13 and 31 are odd as well as prime numbers)

Now complete Q6 Part (b) to Part (d)

Q10: a) 21

Explanation: same as Q6  but in this question ,express the number as the sum of three odd prime numbers.

Solution: 3 + 7 + 11 = 21 (3, 7 and 11 are odd as well as prime numbers)

Complete Q10 Part (b) to Part (d).

HOMEWORK

Q11: Write five pairs of prime numbers less than 20 whose sum is divisible by 5.

(Hint: 3 +7 = 10 ,where 3 and 7 are prime numbers less than 20 and their sum 10 is divisible by 5)

Q7 (enough examples are given in the explanation of Twin primes)

Q12: Fill in the blanks.

That's all for today.

         If you have any doubt, post it in the comment section below.

         Take care.

         GOD BLESS !!