Question

The numbers 17 and 71 are prime numbers Both these numbers have same digits 1 and 7. Find 2 more such pairs of prime numbers below 100 ​

Answer 1

13 and 31

37 and 73

79 and 97

Answer 2

Answer:

Possible 2 digit numbers are:-

13 and 31

17 and 71

37 and 73

79 and 97

As, 17 and 71 is already taken, leave it and check the rest.

Step-by-step explanation:

Let's approach this Question systematically,

These are two digit numbers so each place must contain only a single digit.

Now, at random it could be any 2 numbers, from 1 to 9.

0 is excluded because when the number is reversed the number becomes a 1 digit number.

Ex:-

30 and 03

Here 03 is simply 3, which is a 1 digit number.

So, the possible numbers could be,

1, 2, 3, 4, 5, 6, 7, 8, 9

But it must be a prime number, so all the even numbers can be excluded. This is because any number ending with 0, 2, 4, 6, or 8 is divisible by 2, according to the divisibility rule of 2.

For ex:-

22 is divisible by 2 as it ends with 2,

22 ÷ 2 = 11

So,

We have Possible numbers,

1, 3, 5, 7, 9

Here,

If a number ends with 0 or 5, then its divisible by 5 according to the divisibility rule of 5. So, 5 is also excluded, this is because taking a prime number with 5 is only possible if 5 is in the tens place, but when reversed, it becomes divisible by 5.

For ex:-

53 and 35,

53 is a prime number but 35 is divisible by 5 so it's not.

So,

Possible numbers = 1, 3, 7, 9

Also, we must remember never to take 3 and 9 together, because its sum = 3 + 9 = 12 is a multiple of 3, and so it become a composite number, according to the divisibility rule of 3.

Then,

Possible numbers = 1, 3, 7, 9

Now we can construct 2 digit numbers.

Hence, Possible 2 digit numbers are:-

13 and 31

17 and 71

19 and 91

37 and 73

79 and 97

But 91 is divisible by 7, so the pairs are:-

13 and 31

17 and 71

37 and 73

79 and 97

As, 17 and 71 is already taken, leave it and check the rest.

Now, you can take any 2 pairs, as you wish.

OR

We can simply see all the prime numbers between 1 and 100, and see for such pairs.

Prime numbers between 1 and 100 are:-

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

Hence, Pairs are:-

13 and 31

17 and 71

37 and 73

79 and 97

As, 17 and 71 is already taken, leave it and check the rest.

Hope it helped and believing you understood it........All the best