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Question

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.

Solution
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Given that, $$13$$ and $$31$$ are prime numbers comprising of same digits, $$1$$ and $$3$$.
To fin out: Prime numbers up to $$100$$ which comprises of the same digits.

All prime numbers up to $$100$$ are:
$$2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97$$

In the above list, we can see that there are $$3$$ pairs of prime numbers that comprise of same digits. They are:
$$17, 71$$
$$37, 73$$
$$79, 97$$

Hence, there are $$3$$ more pairs similar to $$13, 31$$. They are $$17, 71,\ \ 37, 73\ and\ 79, 97$$.

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