20100816, 17:02  #1 
Aug 2006
2×29×103 Posts 
Is this guy for real?
http://arxiv.org/abs/1008.2381
This paper makes a fairly extravagant claim: that, on the RH, all primes satisfy for some c and all sufficiently large n. In particular, this is sharper than the heuristic proposed by Cramér and its modification by Maier, and dramatically stronger than the (otherwise) best known bound on the RH, Can someone give an opinion on this paper? I have thoughts about the proof (the key part of which is the case analysis on pp. 78), but I'd rather not bias anyone by speaking on particulars. Further, can I expect the same of the other papers by the same author? http://arxiv.org/find/math/1/au:+Car.../0/1/0/all/0/1 
20100816, 17:12  #2 
"Robert Gerbicz"
Oct 2005
Hungary
5×17^{2} Posts 
That should be wrong, since we have a conjecture from heuristics that limsup((p(n+1)p(n))/log(n)^2)>0. See: http://en.wikipedia.org/wiki/Cram%C3%A9r%27s_conjecture

20100816, 17:52  #3 
Aug 2006
2×29×103 Posts 
I mentioned that conjecture and its 1990 improvement (in the constant)...

20100816, 18:47  #4  
Nov 2003
2^{2}·5·373 Posts 
Quote:
I skimmed a couple of his papers (very superficially). They do not appear to have been written by a crank, but it is suspicious that he does not publish in journals; I only found arxiv and eprint references. The claimed result above, does not "feel" right. And as you observed it is much much stronger than RH is known to imply. 

20100816, 19:15  #5  
Aug 2006
1756_{16} Posts 
Quote:
Plus: Many citations, including the important ones Minus: No apparent mention of the major heuristics contradicted (though see the bottom of p. 1) Plus: Outside the area of concern noted in the first post, the mathematical manipulations seem sound (if routine) Minus: Nonprofessional typesetting  MS Word? Minus: Appears to prove a stronger result, that the prime gap for any fixed k, but this is not mentioned! Minus: Von Koch's result seems to be misstated  I looked up the original to verify!* Minus: Could not find affiliation (in paper or on the web), just lots of arXiv articles On the whole it seemed shady, but not so much that I could be sure on my own so I posted here. We have lots of knowledgeable people here! * "On the assumption that ℜ(ρ) = 1/2, it is certain that " Quote:
Last fiddled with by CRGreathouse on 20100816 at 19:23 

20100822, 17:31  #6  
Jun 2005
2·7^{2} Posts 
Quote:
Quote:
just my thought for the day 

20100822, 17:51  #7  
Aug 2006
2·29·103 Posts 
Quote:
I have *not* come to any conclusions in regard to Carella. I'm pretty convinced that the paper I linked to is wrong, for the reasons outlined above (especially the trouble in the case arguments). Also, I dimly recall a theorem which this would seem to disprove, about the lim sup of g_n over an appropriate denominator. But I'm not sure enough of this to come to a conclusion on my own, thus my question here. As to your particular claim: was I alive in 1905 I would not have labeled Einstein a crank. First of all, I wouldn't have been reading physics papers! Second, there was no doubt surrounding those papers, which closely followed the previous innovations in the field (by, e.g., Lorenz, Poincaré, and Minkowski). If you wanted to make this a challenge, you should have chosen 1915, where there was controversy! Last fiddled with by CRGreathouse on 20100822 at 18:12 

20100822, 23:02  #8 
"Forget I exist"
Jul 2009
Dumbassville
2^{6}×131 Posts 
if I under stand RH = Riemann hypothesis anyways for c to stay constant:
if I did the math correct and I can't find one so far (mind you I probalby haven't searched in the proper range lol). 
20100823, 00:50  #9 
Aug 2006
13526_{8} Posts 
Yes, but I don't think the formula holds. That range is too small for the large gaps.
We expect (Maier 1985) something like infinitely often for every , with while this says that which is smaller by an arbitrary amount. 
20100823, 11:10  #10  
Jun 2005
2·7^{2} Posts 
Quote:
Clearly Don Blazys did not prove TijdemanZagier Conjecture nor Fermat's Last Theorem. However, you label and slander the person and in the same breath you claim he has proven the mentioned conjecture and theorem. Just read what you wrote (I put it in bold). Mathematical logic only tells us that the attempted proof's are flawed or in error, but that does not prove the persons to be a crank or a convincing troll or any of the types listed in the opening sentence! Your statements put you into exactly same league and company as the persons you label. Last fiddled with by AntonVrba on 20100823 at 11:18 

20100823, 12:10  #11 
"William"
May 2003
New Haven
3×787 Posts 
This sounds like you are arguing that the label crank is never justified. If that is what you mean, then I disagree.

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