20051207, 20:16  #23 
Oct 2005
2^{2}·3^{2} Posts 
Thank you to those of you who have proferred a little support. Most of all my thanks go to John Renze whose reply to my question was first, best, and provided a full answer.
RD  You are not my teacher. I am not your pupil. I pity anyone ever put in that position. You may be blessed with the most profound mathematical knowledge and detailed insight into how LL testing works but that does not give you the right to preach at and try to belittle those of us who do not. I have made a point of reading some of your posts in other threads. Your attitude is appalling and your arrogance despicable. I will never, in future, read anything you have posted on any thread. 
20051207, 20:51  #24  
Nov 2003
1110100100100_{2} Posts 
Quote:
Once you come into this forum, professing ignorance, you become a student. I find your attitude appalling. You failed to do even basic required reading. The problem with American education today is that teachers are ALLOWING students to be lazy. They are ALLOWING students to be unprepared. The result is the "dumbing down" of America. My knowledge of the subject DOES give me the right to preach and prattle to someone who asks questions in ignorance. I find *your* attitude to be worthy of total contempt. If you are not willing to do necessary preparation for class, then you have no business in class. When you come here, professing ignorance, this becomes a classroom. If you are not interested in learning, then LEAVE. For my part, I have put YOU into the category of "asks questions when unprepared, therefore is not worth replying to". So let us just leave it as mutual disdain. 

20051207, 21:01  #25  
Nov 2003
2^{2}×5×373 Posts 
Quote:
correctly compute a square root. Suppose the candidate is 3 mod 4. A simple [but extremely expensive] calculation gives a "square root", but the answer will be wrong if the candidate isn't prime. {i.e compute a^(n+1)/4 mod n}. Furthermore, computation of the square root is as expensive as an entire LL test itself! The entire idea is pointless. 

20051208, 08:53  #26  
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
37·281 Posts 
Quote:
I really think we need to separate out the two threads of this discussion. Whether it is possible to "meet in the middle" and whether it is costeffective to do so. As has been pointed out, it is possible. Make the working assumption that the final LL residue is zero and extract square roots. If you fail to find a square root or if the central values don''t match you have a proof of compositeness. As also pointed out, it is not costeffective. Extracting square roots is much more expensive than squaring. Can we put this one to bed now? Paul 

20051208, 11:42  #27  
Nov 2003
2^{2}·5·373 Posts 
Quote:
sized tree of square roots. Storage would be insufficient. 

20051208, 12:36  #28  
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
37·281 Posts 
Quote:
We are in complete agreement that an inconveniently large amount of storage would be required to store the intermediate values for all but the very tiniest problems and so it would not be costeffective. Nonetheless, it could be done in principle, given an open universe and a sufficiently compact encoding method. Let me choose another example. One could, in principle, factor a kilobit RSA public modulus by trial division, if you had enough sufficiently fast machines and were prepared to wait long enough. Compared with NFS, or even QS, it would not be costeffective. On the other hand, there are problems which can not be solved computationally, no matter how many resources are thrown at them and no matter how long they are employed. You gave an example of one on the forum not long ago: computing a real number alpha which can be used to generate the sequence prime numbers. Alpha exists but is not computable, even in principle, with finite resources. Performing a reverse LL test on a specific Mersenne number requires only finite resources, though excessively large. Perhaps you're really an engineer at heart and not a mathematician Paul 

20051208, 14:00  #29  
Nov 2003
2^{2}×5×373 Posts 
Quote:
lengths to hold the tree. 

20051208, 15:13  #30  
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
289D_{16} Posts 
Quote:
Are you denying that we could test M11 by squareroot extraction? The Planck scale is approximately 1e35 metres. The observable universe is around 1e27m across, or about 1e62 Planck lengths. As time goes by, the observable universe becomes larger but let's ignore that for the moment. In three dimensions, we have about 1e186 storage elements if we can find a way of encoding information in spacetime quanta. 1e186 is approximately 2^620  so we could presumably test up to M1201 or so in the spacetime we can see right now. However, earlier I expressed a desire that the universe be open ... I concede that solving the engineering problems would be decidedly nontrivial. Paul 

20051208, 15:28  #31 
"Nancy"
Aug 2002
Alexandria
100110100011_{2} Posts 
We would not need to store the tree, either. Do the forward half of the test, then look for the residue in the tree by traversing it, examining one node at a time. We only need storage equal to the depth of the tree this way. Not that this makes any difference regarding the practicality of the idea... but hey, while we're splitting hairs we might as well split them the whole length.
Alex 
20051210, 00:11  #32 
Aug 2004
italy
113 Posts 
I understand that the all exercise is pointless, but I am curious, and this is probably my opportunity to be jumped on by Bob, or by all of you, for
1) being ignorant 2) not having done my homework 3) being lazy 4) asking stupid questions but I am still unable to work backward starting from 0. Would some kind soul walk me through an example with a very small exponent? 
20051210, 13:09  #33  
Oct 2005
2^{2}·3^{2} Posts 
Quote:
One would have thought that a forum such as this was exactly the place to ask ANY questions and be provided with a RELEVANT answer, but no: According to 'Lord Bob' 1) is not permitted, 2) is mandatory, 3) is tantamount to a criminal offence, 4) is outlawed, and all are reasons to NOT ask one's question. One should NEVER ask a question unless one already knows the answer. Seems to make this forum entirely pointless. 

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