20140822, 04:38  #12 
Jun 2003
1346_{16} Posts 
This is a really slow way of TFing the Mp. The algorithm starts with n=1, and proceeds incrementally, until a factor is found or Mp(2pn+1)^2 becomes negative (which is a fancy way of saying all numbers less than square root of Mp has been checked).
All that is left to prove the theorem is to show that if (2pn+1)  Mp then (6p(2pn+1))  (Mp(2pn+1)^2) which is equivalent of saying 6p  Mp/(2pn+1)  (2pn+1). [I guess the theorem would still be true if the 6p term was not there] Since Mp/(2pn+1) is of the form 2pk+1, Mp/(2pn+1)  (2pn+1) = 2p(kn), so we get the factor of 2p. Therefore we need to show that 3  (kn). ... And here I am out of ideas, so I stop. 
20140822, 05:22  #13 
Jun 2003
1001101000110_{2} Posts 

20140822, 05:56  #14 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2×37×127 Posts 
As we all know, as slow as it is, this algorithm is also at least twice slower than it could have been because only half of the "n" values are eligible to produce a factor.

20140822, 11:53  #15 
"Forget I exist"
Jul 2009
Dumbassville
2^{6}×131 Posts 
if you multiply everything by 2np+1 you get 6p(2np+1)*Mp(2np+1)^3 and this can be reduced to 6p  (2np+1*1)(8*p^3*n^3 + 1) then I tried reducing it using n mod 3 or something but it's that that I think I messed up. edit: this assumes kn to show it's composite.
Last fiddled with by science_man_88 on 20140822 at 12:20 
20140822, 17:18  #16  
Nov 2003
2^{2}·5·373 Posts 
Quote:
It is clear just by reading the abstract/intro that it is a crank effort. Who are these nut jobs? Is Essaadi U. a real University? Are these nut jobs really on the faculty? What kind of fool referee and editor could let this nonsense get published? Or is this a 'pay to publish journal' that accepts anything? 

20140822, 17:22  #17 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2×37×127 Posts 

20140822, 18:28  #18  
Nov 2003
2^{2}·5·373 Posts 
Quote:
What selfrespecting reviewer would ever serve this trash journal? What selfrespecting reviewer would ever accept this trash article? What kind of editor would actually ask someone to act as referee? As editor, I would just bounce the article and not even ask that someone waster their time with it. Just reading the abstract and intro shows that the paper is crap. 

20140822, 19:52  #19  
May 2013
East. Always East.
3277_{8} Posts 
It makes me laugh that they never take S_{n} mod M_{P}.
Quote:
The fact that the modular arithmetic can be used in the algorithm was one of the first things about the process I ever learned. A link to the LucasLehmer Primality Test is pretty easy to find on the Mersenne Prime Wikipedia page. They never referenced the algorithm itself but they referenced mersenne.org when they claimed that the LLT is a good tool, so presumably they would have actually checked out our own page where it is well explained that the residue is taken mod Mp at every iteration... Maybe they all have tenure. Last fiddled with by TheMawn on 20140822 at 20:03 

20140823, 04:18  #20 
"Dana Jacobsen"
Feb 2011
Bangkok, TH
2^{2}×227 Posts 
Not sure whether I should even feed this thread any more...
Looks like this is the last author's bio. I would guess two master's students and the last author as the professor, but it lists them as faculty. I would think with the name attached there would be more concern about the paper (I know my advisor would have been merciless with the red pen even without his name involved). An anecdote that seems apropos: I was attending a master's thesis defense at my school because the subject was interesting. It was about cryptography of some sort, perhaps RSA. I was confused when the performance charts were shown at the end because the key lengths went from 20 to 64. After the faculty questions I asked what units they were  obviously they couldn't be bits, as that would be absurdly small. To the mortification of the advising professor, indeed that was the bit size, because all the work was in Java and Java bigints didn't support needed features, so they just stopped at a key length of 64 bits. Making all the performance comparisons, which was the culmination of their work, moreorless meaningless. 
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