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blackmaled
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Solutions to Polignac's and Twin Prime's Conjecture

May 3rd, 2012, 1:40 pm

I know that there is likely an error somewhere in my solutions to these problems, so I won't be audacious and claim that I have 'the' proof; however, I have been able to convince myself and a few other people with graduate level training in mathematics that this solution is true.I have attached a pdf of my proof here. It is only 4 pages long, reasonably well written, and anybody with basic calculus level understanding should be able to read it.The gist of the proof is that I construct an unbounded matrix C such that the sum of the sum of rows diverges differently then the sum of the sum of columns...if one assumes that the Polignac's or even the Twin Prime's conjecture to be true.I am curious to know what others think of this result and if this is something worth submitting to arxiv? If so I would certainly appreciate an endorsement: Endorsement Code: A4PANW
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Cuchulainn
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Solutions to Polignac's and Twin Prime's Conjecture

May 3rd, 2012, 7:21 pm

Just a suggestion, why not place the post on Numerical Thread or even Brainteaser?OT is mostly populated by poets, musicians and writers.
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trackstar
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Solutions to Polignac's and Twin Prime's Conjecture

May 3rd, 2012, 7:22 pm

QuoteOriginally posted by: CuchulainnJust a suggestion, why not place the post on Numerical Thread?OT is mostly populated by poets and writers.And mad men - we have an ample supply of them too!
Last edited by trackstar on May 2nd, 2012, 10:00 pm, edited 1 time in total.
 
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Cuchulainn
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Solutions to Polignac's and Twin Prime's Conjecture

May 3rd, 2012, 7:23 pm

QuoteOriginally posted by: trackstarQuoteOriginally posted by: CuchulainnJust a suggestion, why not place the post on Numerical Thread?OT is mostly populated by poets and writers.And mad men - don't forget them!Oh yes. We need a Venn diagram. T4A, on the double.
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ExSan
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Solutions to Polignac's and Twin Prime's Conjecture

May 3rd, 2012, 7:40 pm

QuoteOriginally posted by: CuchulainnQuoteOriginally posted by: trackstarQuoteOriginally posted by: CuchulainnJust a suggestion, why not place the post on Numerical Thread?OT is mostly populated by poets and writers.And mad men - don't forget them!Oh yes. We need a Venn diagram. T4A, on the double.most wilmotters are mainly poets, art collectors , music fans etc, then after quants
 
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croot
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Solutions to Polignac's and Twin Prime's Conjecture

May 3rd, 2012, 7:51 pm

Hi, thanks for posting, i enjoyed reading your document.First comment: it seems that 1/2^n could be replaced by any summable positive series?Second comment: p.3 2nd line from the bottom you write "This leads to a contradiction with the earlier result in Equation (5)." Try to provide more grounds to the assertion that both sums should be equal, so we're clear about this.
 
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Cuchulainn
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Solutions to Polignac's and Twin Prime's Conjecture

May 4th, 2012, 8:16 am

First of all, the term "unbounded matrix" does not make mathematical sense. I think you mean "infinite matrices" for which an extensive theory is available.Before making conclusions, you will first need to prove that your infinite matrices exist (necessary and sufficient conditions, e.g. Mirsky). Then conclusions can be made (maybe Perron-Frobenius and matrix splitting) theory since your matrices are positive. Maybe Ascoli-Arzela theorem can be used in the current context.
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MattF
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Solutions to Polignac's and Twin Prime's Conjecture

May 4th, 2012, 9:11 am

Sorry blackmaled but this isn't any good. You can't manipulate infinities in this way and you throw around terms like convergence without any actual demonstrations.You define a number on the basis that there are an infinite number of them then try to claim that this number converges when divided by 2^n. How do you know that? Maybe your infinite set of numbers with the property you want are so rare that the position of them in your matrix dominates 2^n?
 
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Cuchulainn
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Solutions to Polignac's and Twin Prime's Conjecture

May 4th, 2012, 9:49 am

QuoteOriginally posted by: outrunThere is a false postulate that a certain matrix *can't* exist. I think it strange that nobody with "graduate level training in mathematics" spotted something this simple. I don't have any experience with problems like this, but it took me literally 3 seconds to construct a counter example.So the idea has a logical error caused by the false non existence assumption (of a inf x inf matrix not being able to have all column sum to +inf and all rows sum to -inf: -> handling inf calls for special attention)Bravo...Now, from the counterexample, turn the cards around by generalising: find necessary and sufficient conditions for an infinite matrix to exist (btw it has already been done).Example: my take is that matrix B on page 2 exists.
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Cuchulainn
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Solutions to Polignac's and Twin Prime's Conjecture

May 4th, 2012, 10:29 am

QuoteI don't understand what you are trying to say with "existence".i.e. Does the matrix B exist. QuoteThe matrix on page 1 to me simple exists because you can fill it with an algorithm, no? It's a specific instance of a matrix that exists by definition.Not necessarily. QuoteI don't understand "necessary and sufficient conditions". here QuoteTo me the problem is with the assumption that there are no matrices with the *properties* row-sums == -inf && col-sums == +inf.I agree. Can you prove this? Again, I claim that B *does* exist.QuoteA method for proving the existence of a matrices with "row-sums == -inf && col-sums == +inf" without explicitly constructing an example? Bourbaki does it all the time.
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