Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
Seems to me (from skimming the paper) that Earth and the gas giants had orbits stable enough to last until the sun burns out. Of course, if you're planning to move to Mars long term, you might reconsider. Gerhard "It's Not Like Bradbury Said" Paseman, 2015.07.03
Are you trying to block all lines? Or just in the positive quadrant? Also (except for the offset) this is like approximating various reals by p/q where p and q are both primes. Anyway, I expect the answer to differ from that for Polya's problem by a multiplicative constant. Gerhard "Perhaps Pi Squared Over Six?" Paseman, 2015.07.03
Depends on your notion of stable. I'm basing many of my plans on the assumption that civilization will be around long enough to support my children and their children. Gerhard "Knows It's A Risky Assumption" Paseman, 2015.07.03
Do you know of Kummer's theorem (or Lucas's theorem) on binomial coefficients? I think it would be a consequence of one of those. Gerhard "Don't Have A Literature Reference" Paseman, 2015.07.01
If the prime k-tuples conjecture holds, it may be that for infinitely many n that A_n is larger than (log n) /(log log n). Gerhard "Still Too Early To Tell" Paseman, 2015.07.01
Nice and sharp. Once you find out how big a power of two is needed, say $c$ many, you can later establish something like $g(n) \geq g(n + 2^{c-1})/2$. Gerhard "Perhaps Already In The Literature" Paseman, 2015.07.01
It might be great, but it is unlikely. There might be more refined versions of the conjecture in connection with Goldbach's binary conjecture. However, primes fluctuate wildly enough that I would only expect either relation to hold with x and y separated by a significant power of x. For a start, check out texts by Hans Riesel and by Paulo Ribenboim on primes. That and much experimentation may give you a feel for plausible conjectures on distribution of primes. Gerhard "Feels His Way Around Primes" Paseman, 2015.06.30
If you think about how such a conjecture could fail, you could imagine a dense constellation of primes between x and (x+y)/2 and very few primes between (x+y)/2 and y In fact, it is likely that both conjectures fail infinitely often, and conjecture 2 certainly fails for x=y. You might consider running a computer program to check your conjecture for a few million pairs (x,y), to see how it fails. Gerhard "Ask Me About Prime Gaps" Paseman, 2015.06.30
Perhaps it is easier if we remove square roots? Rewriting, I get det(A^4 + ABBA + BAAB + B^4) >= det(A^4 +AABB + BBAA + B^4). While temptingly pleasing, I don't know if positive definite is enough of a restriction to carry this through. Are there similar ineqaulities which are true and motivating? Gerhard "Don't Know About Hermitian Matrices" Paseman, 2015.06.27
The basic intent, of finding out whether the paper is correct, is indeed of interest. That does not mean that it is appropriate for MathOverflow, just as conjectural discussion of Mochizuki's proof of the ABC conjecture and other examples are not appropriate. The previous questions address some of the mathematics and reasons for why the statement might be true or false. The question here does not, and can be viewed as damaging to the author and (more importantly) to MathOverflow. I don't challenge the intent so much as the form. Gerhard "Maybe I Should Just Edit" Paseman, 2015.06.24
Using arXiv trackbacks, one finds other questions and comments on MathOverflow that may be useful in gauging the quality of this paper. If I were the author, I would prefer someone pointing out a specific problem in the current version rather than pointing to older versions and suggesting that insufficient improvements had been made. Gerhard "Treat Authors With Respect Too" Paseman, 2015.06.24
At this current writing, the question is not of the quality I would like to see on MathOverflow. It renders a subjective opinion which may be correct but I will not know without doing some extensive effort. Francesco, If I recall a preprint of yours from ten years ago, and notice a recent publication of a similar paper by you, how appropriate is it for me to publicly claim "Ten years ago it needed a lot of work; can it possibly have gotten publishable?" MathOverflow is not for critiquing papers; it is for answering questions. Gerhard "Let's Not Talk About Publishers" Paseman, 2015.06.24
This is the wrong forum for your question. This kind of question falls in my view to discussing of preprints. If you find a particular error and want confirmation of that error, you might ask about that specific detail. I would avoid editorializing or commenting on the quality of the paper; it should be enough to get people to recognize a serious defect in the paper, if one exists. Gerhard "Treat All Papers With Respect" Paseman, 2015.06.24
I don't know if it is the largest. If you post details in your question, I can think about it and try to improve upon it. Gerhard "Ask Me About Binary Matrices" Paseman, 2015.06.22
