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

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Homework Help Overview

The discussion revolves around the proposition that every prime greater than 7 can be expressed as the sum of two primes minus a third prime. The subject area includes number theory, specifically the properties of prime numbers.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore whether the proposition holds true for specific primes, such as 11. Questions arise regarding the definitions of prime and relatively prime numbers, as well as the validity of using the number 1 in the context of primes.

Discussion Status

There is ongoing exploration of the proposition, with some participants questioning the validity of using 1 as a prime number. A counterexample involving the prime number 11 has been suggested, indicating that the discussion is actively engaging with the original claim.

Contextual Notes

Participants are clarifying definitions and constraints related to prime numbers, particularly the exclusion of 1 from the set of primes, which impacts the validity of the original proposition.

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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Can this be done with 11?
 
Last edited:
Do you mean prime or relatively prime?
 
robert1986 said:
can this be done with 11?

(7+5)-1
 
Robert1986 said:
Do you mean prime or relatively prime?

prime
 
DbL said:
(7+5)-1

1 is not a prime.
 
Curious3141 said:
1 is not a prime.

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.
 
DbL said:
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.

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

Your proposition is disproven.

11 is a counterexample.
 

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