20110820, 19:51  #1 
Aug 2011
nowhere
C_{16} Posts 
Theoretical Model
It seems the problem of finding larger and larger primes is that computer power is the limiting factor. Is it not possible to develop a theoretical model to find and verify larger and larger primes without extensive computation?

20110821, 01:54  #2 
Dec 2010
Monticello
5·359 Posts 
For any theoretical model you care to create (and we'd love to have new ones), the problem is that the amount of computation involved is going to be enormous, because the numbers themselves are enormous. And, even if you did find a model that caused the work to get 10 or 100 times as small, we computational number theorists would simply go out and find larger numbers to work on....
Now, if you want to talk about what that theory might be, I'd point out that the LL test is pretty straightforward. MPQS isn't too bad, but there's only a few here that understand SNFS or GNFS. But I will warn you that you need to do some serious studying, and be smart, even to understand the existing tools. I think some may be game, but I found helping the programming effort to be a lot easier, and even that is slow work for me. 
20110821, 13:47  #3 
"Jason Goatcher"
Mar 2005
3·7·167 Posts 
Another problem for anyone trying to improve the theory is that they decide to present their theory on Mersenne Forum first, which is likely to illicit flames from some of the better educated/unrefined users. I happen to keep in touch with someone who's actively trying to improve the art of number theory in general, and while he might search the forum for help in various things he's working on, he hasn't actually signed in in a very long time.
As it's been said before, while a lesser man may make a lot of mistakes, a greater man will make even more mistakes simply because he continues to try. Last fiddled with by jasong on 20110821 at 13:48 
20110821, 14:05  #4 
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
2×4,787 Posts 
Do you have a true understanding of the size of the numbers we are talking about? They have no real connection to the numbers found in the physical universe. 13,000,000 digits long. The physical universe typically needs less than 100 digits to describe it.

20110821, 14:19  #5  
Dec 2010
Monticello
3403_{8} Posts 
Quote:
http://mersenneforum.org/showthread.php?t=13600 Don't let him get to you. Last fiddled with by Christenson on 20110821 at 14:23 Reason: Added link 

20110821, 17:26  #6  
"Richard B. Woods"
Aug 2002
Wisconsin USA
2^{2}·3·641 Posts 
Quote:
No one has yet come up with one that's more streamlined (asymptotically faster) than LucasLehmer, but there's no proof that a better digital algorithm is impossible. (There is wide skepticism that one is possible, yes, but not proof of impossibility.) Of course, many think that quantum computing should eventually be able to find and verify large primes faster than digital computing can. 

20110821, 19:12  #7  
"Lucan"
Dec 2006
England
2×3×13×83 Posts 
Quote:
But then again, as Feynman, Bohr, Einstein, Born, Borg... have said before: If you think you understand QM, you don't. Or was that the 60s? I've forgotten. David Last fiddled with by davieddy on 20110821 at 19:28 

20110821, 19:18  #8 
Aug 2011
nowhere
2^{2}×3 Posts 
No; I do not have such a model. I apologize for the implication by stating the obvious.
Yes; we are dealing with infinity. I would argue that these numbers do exist in the physical universe just as gravitational singularity at the center of a black hole exists. Within the current state of human knowledge/technology, the persons with the most computing power will find the next largest prime. The human mind is slow but it possesses imagination/creativity and the ability to think about the infinite. 
20110821, 19:22  #9 
"Jason Goatcher"
Mar 2005
DB3_{16} Posts 
The fun thing about quantum computing is that they're managing to add a qubit to what's already working about once every year or 2. So, basically, qubits are advancing at about the rate of Moore's Law, which means they'll be pretty much useless for another 30 years or so. Of course, things might begin to speed up. But, for the moment they're like the science of fusion, it's a future technology, and will be a future technology for a long time.

20110822, 09:06  #10  
Bamboozled!
"𒉺𒌌𒇷𒆷𒀭"
May 2003
Down not across
2×7^{2}×109 Posts 
Quote:
Could you give us some pointers to any literature which contains any experimental or observational evidence to support your claim about the existence of singularities please? Paul Last fiddled with by xilman on 20110822 at 09:07 Reason: Add a singular clarification. 

20110822, 14:24  #11  
Aug 2011
nowhere
2^{2}×3 Posts 
Quote:
The Penrose–Hawking singularity theorems are a set of results in general relativity which attempt to answer the question of when gravitation produces singularities. http://www.ias.ac.in/jarch/jaa/17/213231.pdf 

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