mersenneforum.org  

Go Back   mersenneforum.org > Extra Stuff > Miscellaneous Math

Reply
 
Thread Tools
Old 2021-09-01, 10:20   #276
Dobri
 
May 2018

19910 Posts
Default

Quote:
Originally Posted by tuckerkao View Post
This is exactly the reason why I believe M168202123 has the much stronger prime-like characteristics than M168173321.
This could be interpreted only over finite fields. For a prime p, the finite Galois field GF(pn) has characteristic p. The study of 2p - 1 over GF(pn) is a different topic.

Last fiddled with by Dobri on 2021-09-01 at 10:50
Dobri is offline   Reply With Quote
Old 2021-09-01, 11:40   #277
xilman
Bamboozled!
 
xilman's Avatar
 
"𒉺𒌌𒇷𒆷𒀭"
May 2003
Down not across

3·13·281 Posts
Default

Quote:
Originally Posted by Uncwilly View Post
A number is either prime or it isn't. There is on or off.
True, but you need to specify your number field before pronouncing on any particular number.

In the Gaussian integers 2 is composite and is equal to (1+i)(1-i)

In 𝐙[ √−5 ] 6 = 2*3 = (1+√-5) * (1-√-5) so six is composite with two distinct factorizations.
xilman is offline   Reply With Quote
Old 2021-09-01, 22:54   #278
tuckerkao
 
"Tucker Kao"
Jan 2020
Head Base M168202123

50010 Posts
Default

Quote:
Originally Posted by LaurV View Post
Wow!
That is a big move, from 123 to *23, ten times more exponents.
Check the date and time stamps of the exponents I've worked on for both Trial Factoring and P-1. Hopefully you won't come back and say that UncWilly has used his magic moderator power to modify the data.

Quote:
Originally Posted by mathwiz View Post
You're just not thinking fourth dimensionally dozenally!
The dozenal 7 ender pattern has probably caused LaurV not able to track down the exponents that I've infiltrated.


NF-PM1 and NF up to 278

M168133123 -> Z48383317
M168174323 -> Z483Ӿ312Ɛ <- Reserved by Borek Boissy for PRP test
M168175123 -> Z483Ӿ3697


NF up to 277

M168104323 -> Z4836Ӿ717
M168111523 -> Z48372917
M168114823 -> Z48374807
M168115723 -> Z48375237
M168116323 -> Z48375657
M168117823 -> Z483764Ӿ7
M168121423 -> Z483785Ӿ7
M168122623 -> Z48379227
M168132823 -> Z48383107
M168139123 -> Z48386897
M168149623 -> Z48390987
M168155023 -> Z48393Ɛ27
M168155623 -> Z48394347
M168156523 -> Z48394977
M168160123 -> Z48396Ӿ77
M168163123 -> Z48398757
M168180223 -> Z483Ӿ6627
M168181723 -> Z483Ӿ7477
M168182023 -> Z483Ӿ7687
M168184123 -> Z483Ӿ8937
M168189223 -> Z483ӾƐ887
M168189523 -> Z483ӾƐӾ97
M168191323 -> Z483Ɛ0Ɛ37
M168195523 -> Z483Ɛ3457
M168196123 -> Z483Ɛ3877 <- NF-PM1
M168199123 -> Z483Ɛ5557


F-PM1

M168173323 -> Z483Ӿ2637


I also have the plan to trial factor up the entire avenue of M168,201,*** and M168,202,*** -
https://www.mersenne.org/report_expo...8203000&full=1

Last fiddled with by tuckerkao on 2021-09-01 at 23:32
tuckerkao is online now   Reply With Quote
Old 2021-09-02, 10:00   #279
thyw
 
Feb 2016
! North_America

5816 Posts
Default

Quote:
Originally Posted by tuckerkao View Post
...
I finally picked M168202123 as my headquarter skyscraper because this exponent is very factor-resistant and has a meaning of Search Operation of M168,***,*23 starting year 2021.
168202123 PRP test (~1144 GHzD) assigned on 2021-08-04. Still not finished, but in the meantime, spent ~3272 GhzD of tf and pm1. Too bad you didn't find a factor, so you could throw out your prp test.
Don't know where you got the idea that all those close PM1 105211111 was efficent and to be followed.

Last fiddled with by thyw on 2021-09-02 at 10:01
thyw is offline   Reply With Quote
Old 2021-09-04, 06:10   #280
tuckerkao
 
"Tucker Kao"
Jan 2020
Head Base M168202123

22·53 Posts
Default

Quote:
Originally Posted by thyw View Post
168202123 PRP test (~1144 GHzD) assigned on 2021-08-04. Still not finished, but in the meantime, spent ~3272 GhzD of tf and pm1. Too bad you didn't find a factor, so you could throw out your prp test.
Don't know where you got the idea that all those close PM1 105211111 was efficent and to be followed.
GHz days of the trial factoring run way faster than the GHz days of the PRP tests especially on GPUs like Nvidia Geforce 3080 Ti and 3070 Ti which my gamer friends have.

It seems like that to finish TF of M168202123 from 2^81 to 2^82 has spent only around 3 hours longer at a friend's place than when I run TF 2^77 to 2^78 using my Geforce 780 GTX at my home.

It maybe a good idea to wait for the next generation GPUs such as Geforce 4090 codename Lovelace which will likely be able to work on the range of M461,***,**7. I'm not sure how many days will those take for AMD Threadripper 5970X(Zen 3) to finish up 1 PRP test, or will it be better with 1 more generation to the future like AMD Threadripper 6970X(Zen 4).

The new PRP-Ready exponents -> M168207223 and M168221023.

Last fiddled with by tuckerkao on 2021-09-04 at 06:32
tuckerkao is online now   Reply With Quote
Old 2021-09-04, 12:35   #281
tuckerkao
 
"Tucker Kao"
Jan 2020
Head Base M168202123

50010 Posts
Default

Quote:
Originally Posted by drkirkby View Post
I personally don't feel you are being fair to Ben to ask him to run your exponents.
I didn't understand why you felt the necessity to run a PRP test on M104257709 after it was already assigned to Ben Delo, but you felt it was a waste of time to run a PRP test on a M168M exponent.
tuckerkao is online now   Reply With Quote
Old 2021-09-04, 13:50   #282
Uncwilly
6809 > 6502
 
Uncwilly's Avatar
 
"""""""""""""""""""
Aug 2003
101×103 Posts

22·3·5·167 Posts
Default

Quote:
Originally Posted by tuckerkao View Post
the range of M461,***,**7.
Don't start that range until your current range is finished and proven unprofitable.
Uncwilly is online now   Reply With Quote
Old 2021-09-04, 22:49   #283
tuckerkao
 
"Tucker Kao"
Jan 2020
Head Base M168202123

22×53 Posts
Default

Quote:
Originally Posted by Uncwilly View Post
Don't start that range until your current range is finished and proven unprofitable.
I definitely won't jump to the higher ranges with my current PC, those are simply undoable which a PRP test can cost almost a year. I use M168202123 to record down the GHz days necessary if I ever want to hop to a 100M+ total digits range. I've noticed that the efficiency of P-1 dropped down despite the already larger bounds than the default, perhaps B1 = 2,800,000 and B2 = 120,000,000 will be the correct values to balance the trial factoring depth.

The entire Quadrupler of M168,202,1*9 have been trial factored up 2^77 which locate nearby my Headquarter Skyscraper - https://www.mersenne.org/report_expo...8202189&full=1

Last fiddled with by tuckerkao on 2021-09-04 at 22:52
tuckerkao is online now   Reply With Quote
Old 2021-09-04, 23:19   #284
drkirkby
 
"David Kirkby"
Jan 2021
Althorne, Essex, UK

3×149 Posts
Default

Quote:
Originally Posted by tuckerkao View Post
I definitely won't jump to the higher ranges with my current PC, those are simply undoable which a PRP test can cost almost a year. I use M168202123 to record down the GHz days necessary if I ever want to hop to a 100M+ total digits range. I've noticed that the efficiency of P-1 dropped down despite the already larger bounds than the default, perhaps B1 = 2,800,000 and B2 = 120,000,000 will be the correct values to balance the trial factoring depth.
I'm not sure how you define efficiency. But rather than make assumptions about suitable values of B1 and B2, why not let Prime95 determine them for you? It will know the trial-factoring that has taken place, then selecting B1 and B2 to maximise the result of the equation

chance_of_finding_factor * primality_test_cost - factoring_cost

Personally I would change the saved tests to about 1.05. I assumed that saying it would save 1 test would be optimal, but some results I got on my computer, suggest that indicating to mprime will save 1.05 tests was actually better in some cases. If you make B1 and B2 too large, you will certainly increase your chance of finding a factor, but at a big cost in time for the P-1.

You certainly like doing things that anyone with even a basic understanding of how GIMPS work, will know are not sensible.
  1. Working at 168 million is not sensible
  2. Choosing your own B1 and B2 is not sensible.
drkirkby is offline   Reply With Quote
Old 2021-09-05, 00:04   #285
tuckerkao
 
"Tucker Kao"
Jan 2020
Head Base M168202123

22·53 Posts
Default

Quote:
Originally Posted by Uncwilly View Post
A minor quibble. exponents in the 105M range vs the 110M or 115M range have basically no difference in probability of being a prime. While one might be able to calculate a theoretical difference, the difference is too slight to have a practical consideration, and so far the primes are so scattered and random that we have little real clue when one might be 'due'.
His kit, his joy.
Perhaps around 6~7 years later we'll all have known the answer where the real hidden M52 locates.

exponent of M168202123 - exponent of Real Hidden M#52 = n1
exponent of Real Hidden M#52 - exponent of M105211111 = n2

If n1 is smaller, than I'm correct. If n2 is smaller, than DrKirkby is correct. The 2 skyscrapers should be easy to find for most future generations.

If all exponents from 82589939 to 167999989 are composite, then my dozenal math is correct. If not, then it's wrong.

Last fiddled with by tuckerkao on 2021-09-05 at 00:17
tuckerkao is online now   Reply With Quote
Old 2021-09-05, 02:11   #286
Dr Sardonicus
 
Dr Sardonicus's Avatar
 
Feb 2017
Nowhere

3·1,669 Posts
Default

Quote:
Originally Posted by tuckerkao View Post
I still believe it's possible to bring knowledge across the worlds through the dream. It may be a good idea to try on a simpler toy calculator instead of a complicated scientific computer. Hopefully I'll be able to reach the correct device in my dream just one more time. The less key strokes and time spent, the better the efficiency.

Worlds without the known contacts must use the completely different numerical visual symbols and verbal sounds. Colors and shapes may be the only overlaps to simplify the transformation process.
Dr Sardonicus is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
Automatic fetch of Trial Factoring work for GPU mfakt* LaurV GPU to 72 81 2020-12-02 05:17
Simple Script to get Trial Factoring Work jfamestad PrimeNet 3 2016-11-06 20:32
Why trial factoring work chopped into chunks? lidocorc PrimeNet 4 2008-11-06 18:48
How does the trial factoring work with 15K*2^n-1 jocelynl 15k Search 0 2003-07-11 14:23
How does trial-factoring work? ThomRuley Software 5 2003-05-30 20:34

All times are UTC. The time now is 20:21.


Tue Oct 26 20:21:43 UTC 2021 up 95 days, 14:50, 0 users, load averages: 1.24, 1.29, 1.42

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2021, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.