I’ve read that professor Durán (a mathematician from Venezuela) claims to have the proof of the following conjectures; “There is an infinite number of Mersenne primes” and “there is an infinite number of Fermat primes”, this is the link that i found: http://www.el-nacional.com/sociedad/Venezolano-demostro-teorema-planteado-anos_0_550145051.html, and, As a consequence of it he said that is completly proved the infinity of perfect numbers, these are the papers:

1. Mersenne Primes Cardinality (2013): http://www.open-science-repository.com/mathematics-70081967.html

2. Fermat Primes Cardinality (2014); http://www.open-science-repository.com/mathematics-45011817.html.

I hope you can read this comment and take this seriously enough to post about it.

Capablanca. H

]]>I observed one interesting prime factorization of the three consecutive numbers 2013, 2014 and 2015, 2013=3x11x61, 2014=2x19x53 and 2015=5x13x31, they are all factorized into three distinct primes. I guess there should be no other three consecutive numbers with this property but I can’t find a proof. What do you think? ]]>

I just wanted to say that this is an awesome blog about math. Learned a lot through it. Thank you.

I also wanted to ask you if you could add a link to my website on your link list. It is a free wiki about mathematical proof: http://proofs.wiki/.

Best regards, Brunner Nathan ]]>

I think the moderator should be able to review and cut and paste as much into a post as he/she likes. I have a hint for others, on a problem, but I don’t want to include the entirety of my hint, without a moderator making their own judgment — knowing of course that I have taken the time to write up the hint, in weighing how much of it will be passed along.

]]>You say you want more than a hint, you want a full path laid out? Well, that is like a child asking for you to do his homework when you are the parent.

I will, however, try to help with the incentive structure if a specific, credible request is made by a group (of some defined nature, but not a group closed to new admitted). Some form of joint prize is likely to be necessary; how to ensure that the prize cannot be appropriate by a few is the trick.

As background motivational material, I do not want to see this happen, as recited by Prof. Godfeld at some length — and about which I have seen numerous similar, frankly silly, childish and egotistical attempts to gain individual credit for a process that yields results over time:

http://www.math.columbia.edu/~goldfeld/ErdosSelbergDispute.pdf

That two of the finest mathematicians between 1940 and 1980 should have had such a dispute is evidence of the extreme power of individual incentives, against the collective, unless a structure is put in place to harness those incentives.

One year; I conjecture I can do it in two if folk don’t start posting ideas to form a collective effort to do so, without free-rider incentives, and incentives for people to “cherry-pick” for self-aggrandizement, in blunt terms.

If the challenge is not accepted, I will, reluctantly given my other time commitments, step in and attempt to solve the Twin Prime Conjecture, which, without hints to you, I believe I can do given what I now know within no more than two years.

I look forward to notification that Prof Tao takes this seriously enough to post it as other than a mere comment.

H. Schoenich.

December 22, 2014

Prof. Tao and this participating in the polymath project:

Please permit me to make a few conjectures related to this conjecture, which is the holy grail of the bounded prime polymath project.

After recent work, it is my view that a group of the polymath project should be able to solve the Twin Prime Conjecture within a year if properly organized. The problem is not that difficult, despite the lore. (More on that to come.)

1. Prof. Tao has provided one important element for the polymath project to succeed. That is, a forum for the collection and ready dissemination of information and ideas.

2. The success of the project on bounded gaps depends, as with all polymath projects, on the correct incentive structure. While Prof. Tao has taken the first step, there is no general structure of incentives — simple good will — to give individual contributors with very good ideas an incentive to share them rather than to make them their own. (I will add more about this in a subsequent post if Prof. Tao reposts my post as a main entry for the day, say, tomorrow, December 22.)

3. The best incentive structure for organizing group activity involve incentives where the group and the individual can benefit at the same time. In economics, these result in what are known as Pareto optimal exchanges. That is lacking in the polymath project — it is like saying, “go forth and do good.” It is a nice idea but all kinds of conflicting incentives undermine the collective goal.

4. It is my view, given what I know about the Twin Prime Conjecture, that the collected group of participants in the polymath project on bounded prime gaps could solve the problem within a year.

5. Hint: Bombieri-Vinogradov and Zhang approach are unlikely to yield a solution, if they yield approximations for relatively large bounded gap. That is bounds much greater than 2, 4, or 2^n, for n < 6.

6. If the project does not organize itself with better incentives, I am willing to help. The most powerful incentives are going to encourage (a) monetary self-interest, and (b) sharing of ideas amongst the group — seemingly conflicting goals, but there are well-known ways for creating such incentives in market arenas.

7. I believe I can likely solve the Twin Prime Conjecture within six months but it will require me to put aside other work, and health permitting. I will not provide a better hint than the one in item 5. I am at a stage in life, of an age, and with sufficient professional accomplishments, that my main interest is in seeing the problem resolved. I also have the personal incentive that I would like to see others solve it, and I am quite happy to see others obtain the credit. I would strongly prefer that a polymath group solve it (think Manhattan project — though there the government organized and basically sequestered the group — so they couldn't freelance or avoid sharing insights).

8. If the group of polymath mathematicians forms itself, but does not solve the problem within a year, I am willing to then step in and attempt to solve it. I will not share credit, because it will involve too much personal sacrifice, even if my healthy holds out. I believe I can solve it in six months but certainly no more, at this point, than two years of diligent work — modulo the time needed to convey the ideas in LaTeX format, which always considerably slows down my output. As Montgomery says, "I believe LaTeX is a conspiracy to reduce my productivity." He is definitely correct.

(cont'd)

]]>From visual inspection of your head size and unique shape it is clear you have a huge cranial capacity. You mostly likely wear an extremely large helmet size.

If you would take a head MRI brain scan you will see that your brain has huge volume i.e massive cranial capacity. Just something you should know one day before you pass away.

]]>P.S. If you email me at uldissprogis@gmail.com I can send you a copy of SCIENTIFIC THESAURUS for free. It is my attempt at trying to make language more logical and therefore smarter and less emotionally biased as is the case today with all languages. ]]>

i admire your exposition and your prodigy. I would like to have your suggestion about my present research on number theory specifically about prime numbers. i revisited Wilson’s theorem and generalized it. Among the results that I deduced is the fact that every prime numbers of the form 2n+1 where n is even is a divisor of some number x^2-1. Further proved that x=n! mod 2n+1. What do you think of the result?? thanks ]]>