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

Answer
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Hint: At first, collect and write all the numbers between 1 to 100 and then we observe one by one and see that there are a total of three pairs just like the pair 13 and 31.

Complete step-by-step 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.

Note: Generally, students miss out factors while finding whether a number is prime or composite. So, for a given number n, one should check for the factors up to n2 value. From this, we can also say that we can avoid the numbers ending in 0, 2, 4, 6 and 8 or even numbers in general as they will have factors.

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