20210215, 04:17  #34 
Romulan Interpreter
Jun 2011
Thailand
24A3_{16} Posts 
So, your output, after I fixed the alignment of the printing, to have it in a nice format for easy reading:
And the output after I fixed the math too (k is still limited to 1023, otherwise even more factors will pop up). Do you see any difference? Can you explain why some classes always seems to repeat more often that the other classes? Can you see why you missed a lot of factors at all, and for some exponents you "accidentally" found much larger factors which fit in another class? (therefore, doing more "work"  here quotes are used because all this trouble, albeit extremely slow, still takes only few microseconds). I will let you figure out what change I made. Remark that this method is, as said, extremely slow, it will only find out extremely small factors, and anyhow, who the hack needs trivial factors for over10G expo range? We have headache enough to test those under 1G (Gimps range). Last fiddled with by LaurV on 20210215 at 04:56 
20210216, 00:38  #35  
Feb 2021
Salt Lake City, UT
29 Posts 
Quote:
The LL test is so simple numerically that you can write your own code if you do not thrust mine. It is only more difficult to prove it works especially if you do not want to step out of the integer number space. All these problems are tied to the Last (Great) Fermat Theorem (that a^n+b^n can never be c^n for n>2) which is very difficult to prove and was proven only recently. I rewrote here "my" code in Mathematica with the loop over the exponents. It returns the right values of the primes https://en.wikipedia.org/wiki/Mersenne_prime with exponents below 2000 so it works: Do[ Mp = 2^p  1; s = 4; Do[s = Mod[(s*s  2), Mp]; If[s == 0, Print["PRIME"]; Print[p]], {i, 0, p  2}], {p, 1, 2000}]; PRIME 3 PRIME 5 PRIME 7 PRIME 13 PRIME 17 PRIME 19 PRIME 31 PRIME 61 PRIME 89 PRIME 107 PRIME 127 PRIME 521 PRIME 607 PRIME 1279 Indeed the iteration is done Modulo Mp so s is not growing giant but it works. If s original is 4 then without the Modulo s after p iterations it would be enormously above Mp which is already giant for nontrivial searches only to check if it is its devisor. I say "my" code not my code because it is so simple anyone who has some knowledge of math and Mathematica can write it. Last fiddled with by mattprim on 20210216 at 01:22 

20210216, 00:50  #36  
Feb 2021
Salt Lake City, UT
29 Posts 
Quote:
Last fiddled with by mattprim on 20210216 at 00:59 

20210216, 00:57  #37 
Sep 2002
Database er0rr
3×17×71 Posts 

20210216, 01:23  #38 
Feb 2021
Salt Lake City, UT
29_{10} Posts 
OK. But the list is faster than the frequent calls.
Last fiddled with by mattprim on 20210216 at 01:26 
20210216, 01:28  #39  
Undefined
"The unspeakable one"
Jun 2006
My evil lair
6,121 Posts 
Quote:
Read up about quadratic residues. Last fiddled with by retina on 20210216 at 07:13 

20210216, 07:09  #40 
Romulan Interpreter
Jun 2011
Thailand
83·113 Posts 
I think this guy is trolling. Like, a 7, on a 0 to 10 scale. He doesn't reply to any question, deliberately ignores all the explanation, even if it is done "children level", even after quoting the whole text completely, insists in his mistakes, deliberately write bullshit pieces of code (or to test us?) which he claims to be big inventions, and when caught, blames somebody else. Not my gun, someone else gave it to me, sorry I shot you all... Writing complicate phrases with a lot of technical terms which are irrelevant (irrational bullshit relaed to LL test, and monte carlo, related to TF, haha), just to look "documented". Posting long list of insignificant and small values (repeatedly). Typical troll behavior. Unless he is very young and just learning his stuff, or very stupid, or both. My days of applying Hanlon's Razor for him are gone. I tried my best to explain him what mistakes he does, but it seems he doesn't learn. Out of here.
I would propose the following: One week ban if he posts any of the following:  code piece without code tags  output of the code (lists of small, irrelevant numbers, with lots of spaces) without code tags  any definitive claim about any software or hardware tool, without previous research (like "pari doesn't have this function").  any pompous result realized by himself ("look, I proved this number is composite", followed by a test that takes microseconds). Last fiddled with by LaurV on 20210216 at 07:25 
20210216, 09:29  #41 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
9,391 Posts 
I still think that he is fixing his wristwatch with a bread knife.

20210216, 09:33  #42  
Feb 2021
Salt Lake City, UT
29 Posts 
Quote:
You can find sever proofs of the LL test. Here is for example the paper from Turkey: https://cs.uwaterloo.ca/journals/JIS...lli/kucuk3.pdf with the references to other papers with various methods. Some like the one in the paper are quite cumbersome. The code I posted: Do[ Mp = 2^p  1; s = 4; Do[s = Mod[(s*s  2), Mp]; If[s == 0, Print["PRIME"]; Print[p]], {i, 0, p  2}], {p, 1, 2000}]; runs below 1 minute to early 1950's results but you can compile and run Mathematica in parallel even on IBM Sequoia https://en.wikipedia.org/wiki/Sequoia_(supercomputer) supercomputer https://www.rankred.com/fastestsupe...intheworld/ to sweep the loop much higher even to find the bigger than from 2018. It has 1572864 cores and can also do FFT parallelly partitioning it among them. Last fiddled with by mattprim on 20210216 at 09:49 

20210216, 09:50  #43 
Romulan Interpreter
Jun 2011
Thailand
22243_{8} Posts 
Yes, but what you have implemented is NOT the LL test. The irony is that you are not even able to see the difference
Edit: probably somebody gave you this code too, same as before, and you have no clue what you are talking about. Last fiddled with by LaurV on 20210216 at 09:55 
20210216, 12:43  #44 
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
3^{2}·13·43 Posts 
Last fiddled with by kriesel on 20210216 at 12:48 
Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Searching for m. primes is like playing lottery  joblack  Lounge  20  20090105 15:18 
to be faster at searching mersenne primes  flosculus  Information & Answers  6  20081110 18:59 
searching for Mersenne primes  davieddy  Math  7  20070821 04:51 
A Proposal for searching Recurrence Series Primes  Erasmus  Factoring  3  20040514 09:26 
Need help with math problem re: searching for all primes.  daxm  Miscellaneous Math  5  20030720 19:32 