Maths Olympiad Prep

Track / Stage 3 / 60 of 260 #60 of 1964

Problem 60

AMC 10/12, early questions
Number theory Difficulty 3.2 Multiple choice

In how many ways can 4747 be written as the sum of two primes?

Pick one

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Official solution

For 4747 to be written as the sum of two integers, one must be odd and the other must be even. There is only one even prime, namely 22, so one of the numbers must be 22, making the other 4545.
However, 4545 is not prime, so there are no ways to write 4747 as the sum of two primes A\rightarrow \boxed{\text{A}}.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.