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

  1. Jul 12, 2012 #1


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    "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."

  2. jcsd
  3. Jul 13, 2012 #2
    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
  4. Jul 13, 2012 #3
    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.
  5. Jul 13, 2012 #4
    It's true for all primes between 13 and 9973.
  6. Jul 13, 2012 #5
    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.
  7. Jul 15, 2012 #6


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    But if you subtract 3 from a prime, the result is not necessarily a prime.
  8. Jul 15, 2012 #7
    Right, ignore my posts, I've decided they're nonsense.
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