20160625, 10:19  #1 
Jul 2014
2×3^{2}×5^{2} Posts 
Simon Davis proves existence of infinitely many Mersenne primes?
Hi,
I found this yesterday http://empslocal.ex.ac.uk/people/sta...venperfect.pdf Is this a proof that there are infinitely many Mersenne primes? 
20160625, 13:41  #2 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
3^{3}×367 Posts 
The PDF is almost 10 years old (24Nov2006)!

20160625, 14:20  #3 
Jul 2014
450_{10} Posts 
thanks
If somone can answer my question I'd be pleased . I'm not well enough to understand it. 
20160625, 18:57  #4 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
3^{3}×367 Posts 
That PDF gives an impression of a person who wears a pincenez and speaks in long sentences but periodically uses phrases like "this fact has a profound proctological significance" (instead of "practical"). Many long paragraphs look copied and pasted from other places and make no sense.
Take part 6 (page 15, reproduced below): e.g. it makes an argument that "g(n) is an integer because .... (formula 6.2)". It makes absolutely no sense. Then in the next line g(n) is used already in the modular context (where its existence is obvious, because n 0 (mod n) )... And this sciencelookalike copypastes are used all over, in a similar fashion. 
20160625, 20:48  #5  
Nov 2008
3·13^{2} Posts 
Quote:


20160625, 21:44  #6 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
3^{3}·367 Posts 
Fun fact: two days ago I have been well within 20 or so meters from that article's supplied address (not deliberately, I just was there on other chores).
It is of course the post office. PO Box 13595... I have not looked for it obviously, I was at [I][B]the[/B][/I] post office and CVS pharmacy ...and got sushi at Whole Foods, too. 
20160626, 04:26  #7 
Romulan Interpreter
"name field"
Jun 2011
Thailand
11·911 Posts 
My feelings too. It looks very crankish and mixes a lot of subjects, without connection, but "sounding good", like "geometric representation" of mersenne numbers (?!), trigonometry, pittagorean triplets, Riemann surface, Dirac zero modes, Ramond sectors, inhomogenuous congruence subgroup, Chebyshev polynomials of different kinds, Lagrange interpolations, Lucas and Lehmer series (!?), Goldbach partitions, it looks like all the mathematics I ever heard of are inside that paper. And a lot I didn't hear about, the good part is that I have learned few things googling for some of those names...
Crank for sure. 
20160626, 09:04  #8 
Sep 2003
13×199 Posts 
It's never a good sign of cuttingedge research when half the cited references are four decades old or older, and less than 10% are from this millennium.
Also, Ten Signs a Claimed Mathematical Breakthrough is Wrong 
20160628, 08:15  #9  
Oct 2015
2×7×19 Posts 
Quote:


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