# 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 13, 2012

### willem2

Nope. Try 11.

You can't use 2 for A,B or C because the other 2 primes would be odd and you'd get an even number, so the only primes you can use are 3, 5 and 7. The largest number you can form is 7+5-3 = 9

3. Jul 13, 2012

### Robert1986

He asked this in the homework section, and for some reason he allows the use of 1 so that 7+5-1=11 is a solution. Though, he never explains why we are allowed to use 1.

Of course, if the question is about numbers relatively prime to p, then (p-1)+2-1 is a solution to every prime. But he said that wasn't the case either.

4. Jul 13, 2012

### acabus

It's true for all primes between 13 and 9973.

5. Jul 13, 2012

### acabus

Using Goldbach's conjecture, any even integer is the sum of two primes (at least up to 1.609 × 10^18).

Meaning that (p+3) is the sum of two primes, and 3 can be subtracted to get p.
Or more generally (p+q) is the sum of two primes, where q is a prime number, and q can be subtracted to get p.

I'm not sure how you'd go about making proving it's possible when A is not equal to B.

6. Jul 15, 2012

### HallsofIvy

But if you subtract 3 from a prime, the result is not necessarily a prime.

7. Jul 15, 2012

### acabus

Right, ignore my posts, I've decided they're nonsense.