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

"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?
 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

 Quote by 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
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.

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

It's true for all primes between 13 and 9973.
 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.
 Recognitions: Gold Member Science Advisor Staff Emeritus But if you subtract 3 from a prime, the result is not necessarily a prime.
 Right, ignore my posts, I've decided they're nonsense.