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# the only prime that is the sum and difference of two primes?

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- PuzzlingLv 71 decade agoFavorite Answer
Obviously most primes are odd numbers. The only exception is 2. If you add two odd numbers, you get an even number. If you subtract two odd numbers, you get an even number. That tells us that 2 must be involved in both the addition and subtraction.

In other words.

p = p' - 2

p = p" + 2

p' = p + 2

p" = p - 2

So you need a prime that is part of a sequence of 3 consecutive odd primes. p", p, p'. The only place that happens is with 3, 5, 7. The reason is later on, you'll always have a multiple of 3 within a set of three consecutive odd integers, so you can never have them all being prime.

Answer:

5 = 7 - 2

5 = 2 + 3

- 1 decade ago
3 + 2 = 5

7 - 2 = 5

5 meets the requirements, as 3, 2, and 7 are prime numbers, and 5 itself is a prime number.

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