# Homework Help: Every prime greater than 7 can be written as the sum of two primes

1. Jul 12, 2012

### DbL

"Every prime greater than 7, P, can be written as the sum of two primes, A and B, and the subtraction of a third prime, C, in the form (A+B)-C, where A is not identical to B or C, B is not identical to C, and A, B, and C are less than P."

True?

2. Jul 12, 2012

### Robert1986

Can this be done with 11?

Last edited: Jul 12, 2012
3. Jul 12, 2012

### Robert1986

Do you mean prime or relatively prime?

4. Jul 12, 2012

### DbL

(7+5)-1

5. Jul 12, 2012

### DbL

prime

6. Jul 12, 2012

### Curious3141

1 is not a prime.

7. Jul 12, 2012

### DbL

That is correct.

The number 1 is not considered a prime, although it is a unique integer. The definition of a "prime" number is one that has exactly TWO factors: itself and 1. So the number 1, having only ONE factor, itself, does not meet the definition.

8. Jul 12, 2012

### Curious3141

OK, C (defined to be prime) cannot be 1.

Your proposition is disproven.

11 is a counterexample.