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Number theory Difficulty 4.0 AIME Find the answer United States

Problem:

How many two-digit prime numbers have the property that both digits are also primes?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Solution:

Answer: $4$

When considering the $16$ two-digit numbers with $2, 3, 5$ , and $7$ as digits, we find that only $23, 37, 53$ , and $73$ have this property.

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Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.