Question

Q1. The numbers 13 and 31 are prime numbers. Both these numbers have same digits 1 and 3. Find such pairs of prime numbers up to 100.

Answer 1

Answer:

In the question, we are said that both 13 and 31 prime numbers and both these numbers have the same digits 1 and 3 and thus, we have to find such pairs.

Before proceeding let us know about some information.

The divisors of natural number n are the natural number that divides n evenly. Every natural number has both 1 and itself as a divisor and if a number has no divisor other than 1 and itself it is considered as prime otherwise, it is considered as composite. Now, let's consider examples like 5, its factors are only 1 and 5, so, it’s a prime number, while, for 4 it's factors are 1 and 4 as well as 2. Hence, it is considered as composite.

So, we will first write down all the prime numbers between 1 and 100.

The primes 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.

Here pairs are:

13 and 31, 17 and 71, 37 and 73.

The pairs except 13 and 31 are 17 and 71, 37 and 73.

Step-by-step explanation:

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