tag:blogger.com,1999:blog-20067416.post1358481744658115922..comments2023-12-21T06:35:36.624-05:00Comments on Recursivity: Twin-Prime Problem and Goldbach Conjecture Solved?Unknownnoreply@blogger.comBlogger43125tag:blogger.com,1999:blog-20067416.post-80649618606672234892018-02-02T13:10:10.748-05:002018-02-02T13:10:10.748-05:00Ken, that's not original with you. See http:...Ken, that's not original with you. See http://oeis.org/A007534Jeffrey Shallithttps://www.blogger.com/profile/12763971505497961430noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-69315349956804322812018-02-02T12:57:32.430-05:002018-02-02T12:57:32.430-05:00I do not get it ... please elaborate further
I do not get it ... please elaborate further<br /><br />Anonymoushttps://www.blogger.com/profile/17960004026240335780noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-11764998526065632562018-01-30T08:48:29.994-05:002018-01-30T08:48:29.994-05:00Forget proofs of the Goldbach and Twin Primes Conj...Forget proofs of the Goldbach and Twin Primes Conjectures. But here is a very nice connection between them. It's a way stronger version of the Goldbach Conjecture.. http://www.math-math.com/2018/01/goldbach-conjecture-meets-twin-prime.htmlKen Abbotthttps://www.blogger.com/profile/07654085244823197611noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-17851225047340595222016-07-20T16:35:24.053-04:002016-07-20T16:35:24.053-04:00I was talking about output size in bits, not numbe...I was talking about output size in bits, not number of solutions.Jeffrey Shallithttps://www.blogger.com/profile/12763971505497961430noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-80507214835336347842016-07-20T08:59:38.110-04:002016-07-20T08:59:38.110-04:00Professor Shallit
I won't bother you anymore....Professor Shallit<br /><br />I won't bother you anymore. The output is proportional to N/logN the approximate # of primes less than or equal to N, for even #2N Unknownhttps://www.blogger.com/profile/03473803205462286154noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-86712491756111908662016-07-20T08:50:06.326-04:002016-07-20T08:50:06.326-04:00Professor Shallit
The algorithm presented in the p...Professor Shallit<br />The algorithm presented in the paper sieves through primes less than or equal to N, where 2N is the number in question. I do not see how this could possibly be done in logN<br />since you do have to look at all these primes as potential solutions.<br />Unknownhttps://www.blogger.com/profile/03473803205462286154noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-60240018451597238092016-07-20T07:28:19.825-04:002016-07-20T07:28:19.825-04:00It's completely trivial to find all solutions ...It's completely trivial to find all solutions for a given number. And it cannot be done efficiently (in log N) because the output size in bits is almost certainly something like N. So it has no interest for anyone.Jeffrey Shallithttps://www.blogger.com/profile/12763971505497961430noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-76126089075248490022016-07-20T07:23:21.504-04:002016-07-20T07:23:21.504-04:00
Professor Shallit
Would you please take a look at...<br />Professor Shallit<br />Would you please take a look at a very short paper (2 pages) by Matilda Walter - <br />On finding all solutions to the Goldbach problem for 2N - vixra.org 1607.0359 <br />The paper does not claim a proof of G.C.,in fact it explicitly disclaims it. It presents an algorithm finding all solutions for a given even number. <br /><br />Regards<br />M.w. Unknownhttps://www.blogger.com/profile/03473803205462286154noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-54896944749512842192016-06-13T18:42:43.851-04:002016-06-13T18:42:43.851-04:00Mr Adraktas, should I suppose that by "Mr Kon...Mr Adraktas, should I suppose that by "Mr Konstandakatos" you refer to me? If so, you got my name wrong. I tried to look at your paper. But that site is the most annoying site I've ever seen. It started asking my identity, my occupation, it asked me to upload a paper, etc. I'm not interested in proving to the site who I am before taking a look at your paper. The very fact that your paper is uploaded on a commercial site fishing for data makes it fishy. Anyway, I insisted and downloaded your paper and as soon as I saw it I exclaimed "holy shit!" OK, this is its content. I reproduce it here in its entirety:<br /><br><br />Goldbach's conjecture proven and in a neat and brief way by Constantine Adraktas<br><br />Every even integer greater than 2 can be expressed as the sum of two Primes<br><br />All the Prime numbers (bar 2 and 3) reside in the [ 6α + 5 ] and [ 6α + 7 ] vectors<br><br />[ 6α + 5 ] = [ 6α + 6 ] - [ 1 ] and [ 6α + 7 ] = [ 6α + 6 ] + [ 1 ]<br><br />There are 3 possible sums ( Σ ) combinations involving these vectors<br><br />Σ of each element of [ 6α + 5 ] with each element of [ 6α + 5 ] producing the [ 6α + 4 ]<br />vector bar the number 4<br><br />Σ of each element of [ 6α + 5 ] with each element of [ 6α + 7 ] producing the [ 6α + 6 ]<br />vector bar the number 6<br><br />Σ of each element of [ 6α + 7 ] with each element of [ 6α + 7 ] producing the [ 6α + 8 ]<br />vector bar the number 8<br><br />The [ 6α + 4 ] - [ 6α + 6 ] - [ 6α + 8 ] vectors cover all the even integers hence the 3 sums<br><br />above cover all the even integers (bar 4 - 6 - 8 which are the sums of 2 + 2 - 3 + 3 - 3 + 5<br />that is the sums of Primes)<br><br />QED .... Goldbach's conjecture proven and in a neat and brief way<br /><br><br /><br />I think that what Jeff Shallit is trying to tell you is that there is no chance in a trillion that what you wrote can be considered a mathematical proof of a theorem. To make an analogy, what he's saying is that you behave like someone who listened to great pianists perform Rachmaninoff's Piano Concertos who, one day, decided to play it himself too without ever having played anything on the piano before. Something like that. Or it's like me going to Olympic Games and pretending I got the gold medal in weight lifting. I can't do it.Takis Konstantopouloshttps://www.blogger.com/profile/14675216467783238403noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-79677954538180576492016-06-13T17:59:56.666-04:002016-06-13T17:59:56.666-04:00What part of "go away" don't you und...What part of "go away" don't you understand?<br /><br />I'm not Canadian.<br /><br />You still don't understand anything about randomness or what is meant by the primes behaving randomly.Jeffrey Shallithttps://www.blogger.com/profile/12763971505497961430noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-11915383287876077052016-06-13T17:57:01.637-04:002016-06-13T17:57:01.637-04:00Manners and proper language Mr Shalit
And if you a...Manners and proper language Mr Shalit<br />And if you and Mr Konstandakatos object to my using the term "random primes" I would like to suggest you mention that in here<br /><br />https://terrytao.wordpress.com/2008/02/07/structure-and-randomness-in-the-prime-numbers/#comment-276583<br />and teach a lesson to Professor Tao ... as a Canadian hopefully you have a sense of British humour<br />Constantine.Adraktas@MIT-Partners.eu<br />Anonymoushttps://www.blogger.com/profile/17960004026240335780noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-74597511020084979102016-06-13T17:42:42.366-04:002016-06-13T17:42:42.366-04:00Go away, you are boring and unwilling to learn.Go away, you are boring and unwilling to learn.Jeffrey Shallithttps://www.blogger.com/profile/12763971505497961430noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-36304239916151921752016-06-13T13:18:38.849-04:002016-06-13T13:18:38.849-04:00"I have no interest in youtube videos ... You..."I have no interest in youtube videos ... You're behaving like a crackpot". Is Prof Terence Tao a crackpot since he is using U Tube for one of his most famous lectures?<br />Also Prof Richard Taylor of IAS ? It is an IAS video !<br />https://www.youtube.com/watch?v=5pTaZu3C--s<br />Anonymoushttps://www.blogger.com/profile/17960004026240335780noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-32279041046601608212016-06-13T12:52:25.180-04:002016-06-13T12:52:25.180-04:00Sorry but it is not a whatever U Tube ... it is a ...Sorry but it is not a whatever U Tube ... it is a lecture Prof Terence Tao has given in several places ... he knows mathematics ... correct ?<br />Anonymoushttps://www.blogger.com/profile/17960004026240335780noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-26531600936406095472016-06-13T12:06:50.948-04:002016-06-13T12:06:50.948-04:00No, I have no interest in youtube videos. If you ...No, I have no interest in youtube videos. If you are talking about mathematics, cite results in papers or books, not videos. You're behaving like a crackpot.Jeffrey Shallithttps://www.blogger.com/profile/12763971505497961430noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-53984389759769073522016-06-13T12:02:45.018-04:002016-06-13T12:02:45.018-04:00So what? Did Don Zagier claim a proof of "th...So what? Did Don Zagier claim a <i>proof</i> of "the prime numbers are random"? No, he didn't. He was just speaking metaphorically.<br /><br />Your problem is that you have no understanding of what Zagier was saying. Jeffrey Shallithttps://www.blogger.com/profile/12763971505497961430noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-29951533316220927392016-06-13T11:51:33.240-04:002016-06-13T11:51:33.240-04:00please see this by Professor
on prime randomness
h...please see this by Professor<br />on prime randomness<br />https://www.youtube.com/watch?v=PtsrAw1LR3E<br /><br />Anonymoushttps://www.blogger.com/profile/17960004026240335780noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-54334102218253153712016-06-13T10:37:30.569-04:002016-06-13T10:37:30.569-04:00Allow me to refer you to Professor Zagier
In a 19...Allow me to refer you to Professor Zagier<br /><br />In a 1975 lecture, Don Zagier commented <br /><br />"There are two facts about the distribution of prime numbers of which I hope to convince you so overwhelmingly that they will be permanently engraved in your hearts.<br /><br />The first fact is that, despite their simple definition and role as the building blocks of the natural numbers, the prime numbers grow like weeds among the natural numbers, seeming to obey no other law than that of chance, and nobody can predict where the next one will sprout<br /><br />The second fact is even more astonishing, for it states just the opposite: that the prime numbers exhibit stunning regularity, that there are laws governing their behavior, and that they obey these laws with almost military precision" (Havil 2003, p. 171)<br />Anonymoushttps://www.blogger.com/profile/17960004026240335780noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-50414100712555208442016-06-13T09:07:13.088-04:002016-06-13T09:07:13.088-04:00It's amazing, isn't it, that someone would...It's amazing, isn't it, that someone would use phrases like "Prime Numbers, the building blocks of the Composite Numbers, are not Random Numbers" in trying to support an, allegedly, mathematical proof. That's why the world is coming to an end. :-) People don't understand elementary concepts.Takis Konstantopouloshttps://www.blogger.com/profile/14675216467783238403noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-12604351025592498512016-06-13T08:26:00.708-04:002016-06-13T08:26:00.708-04:00You don't understand what it means when a math...You don't understand what it means when a mathematician says "the primes are distributed randomly". It is not a formal statement; it is more an imprecise claim about the distribution of primes. For example, if you look at the primes modulo 4, the primes are roughly equidistributed in the residue classes 1 and 3. There are, of course, limits to this kind of randomness.<br /><br />It is a completely false claim to say "all famous Mathematicians consider them to be Random Numbers". Jeffrey Shallithttps://www.blogger.com/profile/12763971505497961430noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-90538859280337809102016-06-13T05:15:58.459-04:002016-06-13T05:15:58.459-04:00nevertheless take a look at it
Also take look at t...nevertheless take a look at it<br />Also take look at the following ... primes are not random<br />The Fundamental Theorem of Arithmetic and proving that the Primes are not Random by Reductio ad Absurdum - By Constantine Adraktas, MIT Alumnus<br /><br /><br />The Prime Numbers have been tormenting famous Mathematicians since antiquity and all famous Mathematicians consider them to be Random Numbers. <br /><br />Lectures given by Professors Richard Taylor and Terence Tao and testify to this belief (see their lectures in U Tube under "Primes and Equations | Richard Taylor - Videos from the Institute of Advance Study" and "Terence Tao: Structure and Randomness in the Prime Numbers, UCLA" respectively). <br /><br />However, using the Fundamental Theorem of the Arithmetic, also called the unique factorization theorem or the unique-prime-factorization theorem, states that every Integer Number greater than 1 is either a Prime Number itself or is the product of Prime Numbers and that this product is unique, up to the order of the factors.<br /><br /> <br />one concludes that the Prime Numbers, the building blocks of the Composite Numbers, are not Random Numbers.<br />Proof<br />Set all αi = 1 and keep at least two primes pi <br />The emerging products combinations are Composite Number, ie not Random Numbers<br />Hence by Reductio ad Absurdum it is proven that the Primes are not Random, as Order (Composite Numbers) cannot be created by Randomness - Chaos (Prime Numbers)<br /><br />Author<br />Constantine Adraktas, MIT<br />constantine.adraktas@mit-partners.eu<br />Telephone: 00 - 30 - 6944 - 314 - 309<br />Anonymoushttps://www.blogger.com/profile/17960004026240335780noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-81914658696457136862016-06-13T05:10:49.751-04:002016-06-13T05:10:49.751-04:00Without even looking at it I can tell you it's...Without even looking at it I can tell you it's wrong.Jeffrey Shallithttps://www.blogger.com/profile/12763971505497961430noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-67737012599554692402016-06-13T05:04:20.661-04:002016-06-13T05:04:20.661-04:00I was looking forward to your considerate opinion ...I was looking forward to your considerate opinion Mr ShallitAnonymoushttps://www.blogger.com/profile/17960004026240335780noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-45339510251610800252016-06-13T05:00:39.132-04:002016-06-13T05:00:39.132-04:00It's completely inappropriate to post a paper ...It's completely inappropriate to post a paper to the comments of a blog. Use the arxiv, or vixra, to post your papers.Jeffrey Shallithttps://www.blogger.com/profile/12763971505497961430noreply@blogger.comtag:blogger.com,1999:blog-20067416.post-55426277904952814832016-06-12T15:21:37.122-04:002016-06-12T15:21:37.122-04:00did you see the paper text I uploaded as to evade ...did you see the paper text I uploaded as to evade Academia in your case ?Anonymoushttps://www.blogger.com/profile/17960004026240335780noreply@blogger.com