20051210, 15:18  #34  
Aug 2004
italy
113 Posts 
Quote:
That is how this forum should work, and I have seen many examples of that in previous posts, even from Bob Silverman. Last fiddled with by ppo on 20051210 at 15:20 

20051210, 16:54  #35  
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
23621_{8} Posts 
Quote:
Ask Bob a sensible question and he will give a sensible answer. I suggest that you read through his responses to people who have asked sensible questions earlier. And yes, I do mean "sensible" and not "advanced". He has answered questions before now that required only very simple mathematical concepts to answer. Asking stupid questions, on the other hand, is guaranteed to annoy Bob (and irritate many other people, for that matter). Being able to distinguish between sensible and stupid questions becomes much easier if you've done your homework. Paul 

20051211, 02:52  #36  
Jun 2005
2·191 Posts 
Quote:
Don't let Bob get to you. Hopefully someday he'll recognize that there's more value to a person than how little they know about his particular field of interest, and develop some people skills. Let's use the previously quoted example of 2^71, which is 127. To do the forward test, start out with S0=4. Each successive iteration is the square of the previous minus 2, mod 127. S1 = S0*S02 = 4*42 = 14 S2 = 14*14  2 = 194 = 67 mod 127 Since we're interested only in modulus 127, which is the remainder of a division by 127, we get 67 (194/127 = 1 remainder 67) S3 = 67*67  2 = 4487 = 42 mod 127 S4 = 42*42  2 = 1762 = 111 mod 127 S5 = 111*111  2 = 12319 = 0 mod 127 When we get to 5, which is n2, we stop. If it's zero, then the number is prime. Yipee! Now, assuming we start by assuming S5 = 0, how can we work backwards to get S4? Well, we solve for S4: S5 = S4^2  2 S4 = sqrt(S5 + 2) = sqrt(2) We need to know the square root of 2 using the mod 127 field. In this field, 2 can have any of the following values: 2 127+2=129 127*2+2=256 127*3+2=383 127*4+2=510 . . . 127*125+2 = 15877 So there are many values which can be possible square roots. We're only interested in the above values that are perfect squares, since our number field contains only integers. In the set defined above, the values 256 and 12319 are both perfect squares of 16 and 111. I created a spreadsheet to work that out, and the computation for this is much more involved than the squaring and subtracting used for the forward step. What's more is that you end up with two answers! The backward step is not deterministic. You need to consider both of these possibilities as being potential S4 values, which leaves exponentially more possibile values as you go a given number of steps backward. The simple fact is that by the time you perform even 1 backwards iteration, you could solve the entire problem using the forward steps. Heck, with numbers as large as we're testing, I don't think the universe is old enough to have perform one iteration. We'd need to evaluate over 2^10000000 square roots. Drew Last fiddled with by drew on 20051211 at 03:07 

20051211, 09:12  #37  
Aug 2004
italy
113 Posts 
Quote:
By the way I think that Bob is only jumping on people when he has some evidence that they are not doing at least some effort to think to the problem before posting..and I WAS indeed lazy, so please everyone jump hard on me... (PPO, write one hundrede times, I was lazy, I was lazy, I was... ) Let me explain: Being lazy as I am, tonight I decided to work on an example starting from the smallest exponent: 3, and working backward, I reached immediately an S0 value of 3, not 4, so I suddenly realized that, let aside computational difficulties, there is a more compelling reason why the meet somewere in between method cannot work: since there are different starting values for the LL sequence, all leading to an ending value of 0 for a Mersenne prime, there is an high probability that the forward and the backward methods will never meet. That should have been evident to me days ago, but , as I admit, I was too lazy to think... 

20051211, 14:24  #38  
Feb 2004
France
1110010010_{2} Posts 
Quote:
The paper of Vasiga/Shallit (see: LLT DiGraph in Mersenne wiki for details and links) gives information about the tree and the loops, but not about the starting values. Who can add something about these "starting values" in the wiki ? Tony 

20051215, 09:06  #40  
Feb 2004
France
392_{16} Posts 
Quote:
And MathWorld does not say a word about these starting values. The same in "The Little Book of Bigger Primes" of Ribenboim. Could someone (with better Number Theory skills than me) could propose MathWorld to add information about these starting values ? with links to papers and proofs ! Tony 

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