- #1
Mollet1955
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if u have 3 primes: x,y,z
then prove its sum m=x+y+z is unique ? Thank you
then prove its sum m=x+y+z is unique ? Thank you
Proving the Uniqueness of the Sum of 3 Primes
- Context: Undergrad
- Thread starter Mollet1955
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- Primes Sum Uniqueness
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Discussion Overview
The discussion revolves around the uniqueness of the sum of three prime numbers. Participants explore whether a given sum, derived from three primes, can be achieved by other distinct sets of three primes.
Discussion Character
- Debate/contested
- Mathematical reasoning
Main Points Raised
- One participant initially asks for a proof of the uniqueness of the sum of three primes.
- Another participant points out that the sum of any three numbers is unique, suggesting the question may be misphrased.
- A clarification is made that the question seeks to find other sets of three primes that sum to the same total.
- Some participants propose that it is indeed possible to find multiple sets of three primes that can yield the same sum, citing examples with numbers less than 20.
- One participant mentions the possibility of infinitely many counterexamples, particularly in relation to twin primes.
- There is a suggestion that adding the same prime to different pairs could yield valid sums, though this is met with some confusion.
- Another participant expresses frustration with the complexity of the problem, indicating a struggle to progress in the discussion.
Areas of Agreement / Disagreement
Participants do not reach a consensus on the uniqueness of the sum of three primes, with multiple competing views and examples presented throughout the discussion.
Contextual Notes
Some assumptions about the nature of primes and their sums remain unexamined, and the discussion does not resolve the mathematical intricacies involved in proving or disproving the uniqueness of such sums.
- #2
matt grime
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As stated it is a none question: given any three numbers there is a unique number that is their sum.
- #3
Mollet1955
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Oh I stated probme incorectly,
let x,y,z be primes, m=x+y+z
Can u find other three primes that can sum to get m ? m can be any number.
let x,y,z be primes, m=x+y+z
Can u find other three primes that can sum to get m ? m can be any number.
- #4
matt grime
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Of course you can. You should try it. It's possible to find infinitely many counter examples, and there is a number less than 20 that is the sum of two primes in two different ways.
- #5
Tide
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matt grime said:
Yes, but the question concerns three primes!
- #6
shmoe
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Tide said:Yes, but the question concerns three primes!
So add the same prime to both pairs.
- #7
Tide
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shmoe said:
Of course. Nevermind!
- #8
ramsey2879
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I think that by other you have to find three totally different primes.Mollet1955 said:
This too is easy 3+13+31 = 7+11+29. Again, using 3 and 7, and two sets of twin primes. there are infinitely many examples assuming that their are infinitely many pairs of twin primes.
- #9
Mollet1955
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If so, I think I can't go on solvin this problme
Clearly a simple sum repeated day after day, trying to complicate the main porblme
Clearly a simple sum repeated day after day, trying to complicate the main porblme