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

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Discussion Overview

The discussion revolves around the proposition that every prime greater than 7 can be expressed as the sum of two primes, with the additional condition of subtracting a third prime. Participants explore the validity of this claim through examples and counterexamples, touching on related concepts such as Goldbach's conjecture.

Discussion Character

  • Debate/contested
  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • One participant proposes that every prime greater than 7 can be expressed in the form (A+B)-C, where A, B, and C are distinct primes less than P.
  • Another participant counters this by using the example of the prime number 11, arguing that the largest sum achievable with the primes 3, 5, and 7, while adhering to the conditions, is 9.
  • A subsequent reply reiterates the example of 11, noting that the inclusion of 1 as a prime in the homework context allows for a solution of 7+5-1=11, but questions the rationale behind using 1.
  • One participant claims that the proposition holds true for all primes between 13 and 9973.
  • Another participant references Goldbach's conjecture, suggesting that any even integer can be expressed as the sum of two primes, which could relate to the original claim when considering the subtraction of a prime.
  • A participant raises a concern that subtracting 3 from a prime does not guarantee that the result is also a prime.
  • One participant later dismisses their previous contributions as nonsensical.

Areas of Agreement / Disagreement

Participants express disagreement regarding the validity of the original proposition, with some providing counterexamples and others supporting the claim for certain ranges of primes. The discussion remains unresolved, with multiple competing views presented.

Contextual Notes

There are limitations regarding the definitions of primes and the inclusion of 1 as a prime in the context of the discussion. Additionally, the implications of Goldbach's conjecture are not fully explored in relation to the original claim.

DbL
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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."

True?
 
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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
 
willem2 said:
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.
 
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.
 
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.
 

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