mersenneforum.org Getting others to do the work on exponents I like (was: Trial Factoring Progress)
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 2021-10-18, 11:52 #342 tuckerkao   "Tucker Kao" Jan 2020 Head Base M168202123 1111101102 Posts I like this semiprime with the interesting double-double format nearby the right end: 13,898,772,659,372,959 [decimal] 59 = [dozenal] 4Ɛ Attached Thumbnails   Last fiddled with by tuckerkao on 2021-10-18 at 12:18
2021-10-18, 20:07   #343
tuckerkao

"Tucker Kao"
Jan 2020

2×251 Posts

Quote:
 Originally Posted by mathwiz There is no actual math to support the claim that your proposed exponent range is any more likely, or any less likely, to contain a Mersenne prime. My only hope is that others aren't led down this pointless crusade, and just keep their mprime / Prime95 clients receiving whatever assignments the server hands out.
There are very few exponents left in the M105M and M106M waiting to be PRP tested, chance the hidden Mersenne Prime is locating there has significantly dropped, remember how hard DrKirkby wanted to hop on those exponents before he quit GIMPS before it restricted him to the Cat 4 assignments due to some suspected result issues.

Ben Delo's wave-front is around M107.1M and the UncWilly drought still persist with less than a full year to go to become the longest gap of discovering a new Mersenne Prime after the previous one. Even M116M and M117M seems to be too long to work on for DrKirkby despite the request from Zhangrc to ask him to stay and just play more casually.

Quote:
 Originally Posted by Dr Sardonicus
Base 5 dozens with a dozenal superbase is still somewhat different than Base sixty with a decimal superbase.

Since it's probably not possible to use base sixteen to figure out how the residue values of a PRP tested exponent relates to the location of a hidden Mersenne Prime. It's okay to try on base 1 dozen 4.

Quote:
 Originally Posted by tuckerkao M168,*8*,*23 without known factors:
At least this list isn't too long for me to finish, but still too many to allow only 5 guesses from Mathwiz.

Quote:
 Originally Posted by sweety439 The number of Mersenne exponents end with Ɛ should be less than that of Mersenne exponents end with 1, 5, or 7, this is because for all Sophie Germain primes p == 3 mod 4 (all such primes end with Ɛ), Mp is divisible by 2*p+1, thus Mp is composite.
There are much fewer English words that start with Q, but Qu is a pair of interest that links to where the common words locate. I'm pretty sure I don't want to leave out the dozenal 4Ɛ ender candidates especially when they show the same numerical patterns in base 5 dozens too.

I'm assuming if the next hidden Mersenne Prime really ends with Ɛ, then it has the higher chance to be 4Ɛ for the final 2 digits dozenally.

Quote:
 Originally Posted by LaurV like "M11.44M is a double double" (???) like a bot would do (i.e. looking at the patterns on my post and reply things with the same pattern but having nothing to do with the subject semantically).
The numbers with the double double patterns are sometimes lucky, I only hope 1 of the results can be P-PRP for the co-factors.

Quote:
 Originally Posted by VBCurtis It's "possible" to do anything we want. It's our project. Your P-PRP thought is gibberish, but it seems that doesn't trouble you.
If I have AMD Threadripper 5970X with Nvidia Geforce 3090 Super, I should be able to finish 1 M168,***,*23 exponent every 4~5 days. The M168,*8*,*23 list will only last several months. The only reality that will trouble me is the supply shortage that'll prevent me from purchasing the PC I want, thus unable to prove myself.

Last fiddled with by tuckerkao on 2021-10-18 at 20:39

2021-10-19, 12:43   #344
Dr Sardonicus

Feb 2017
Nowhere

139516 Posts

Quote:
 Originally Posted by tuckerkao Also in base 5 dozens, the dozenal 4Ɛ enders(as a regular number) frequently come directly 1 less than a very composite number.

This is gobbledygook3. Whether a number is one less than a highly composite number does not depend on what base you express it in. The term "dozenal enders" implies base twelve. A 2-digit ending in base twelve would be a congruence class modulo 144. Assuming "base 5 dozens" means "base sixty" a given congruence class mod 144 would correspond to 25 possible 2-digit endings in base sixty. I have no idea what you mean by "as a regular number," but the phrase uses the singular "number" in referring to the plural "dozenal enders" so is ungrammatical.

Assuming your excessively obscure notation "dozenal 4Ɛ enders" means "numbers congruent to 59 modulo 144", adding 1 to such a number gives 12 times a number congruent to 5 (mod 12).
Quote:
 Originally Posted by tuckerkao Base 5 dozens with a dozenal superbase is still somewhat different than Base sixty with a decimal superbase.
Base sixty is base sixty. Also, one radix or base that is a multiple of a given base is a "superbase" of the given base. You have it the wrong way around.

2021-10-20, 23:50   #345
tuckerkao

"Tucker Kao"
Jan 2020

50210 Posts

Quote:
 Originally Posted by chalsall You post here at the Mersenne Forum. Therefore, you consume my time. Deal with it.
The range from M57885161 to M74207281 seems to be a very busy area. Lots of users pass through here everyday. I only showed up once nearby this area and other people complained about my activity.

I probably made louder noises than greenskull very many times but because of my exponent location. People can hardly hear unless they are working above M166M or below M170M, only Dobri has showed up nearby during the past 1 month.

Quote:
 Originally Posted by greenskull Well, at least someone stood up for me. May good luck and happiness accompany you in everything my friend! Let 52nd Mersenne Prime be yours :)
It's most likely hidden in an outskirt area where not a lot of activities are going on today. I only hope I've already purchased this land slot. I have 500+ exponent deeds that include my trial factoring entries as of today.

You probably should declare your very personal range in a rural exponent area where it'll be large enough to own a project thread.

The logic is really simple because no other Mersenne users beside me are interested in working on any exponents from M168286031 to M168286997 https://www.mersenne.org/report_expo...8287000&full=1, so I can name this avenue with whatever the title I like (such as Dozenal Behemoth Avenue) and others won't rally the protests at all.

Last fiddled with by tuckerkao on 2021-10-21 at 00:32

 2021-10-21, 22:48 #346 tuckerkao   "Tucker Kao" Jan 2020 Head Base M168202123 2×251 Posts After Dobri finished P-1 on an exponent with only TF up to 2^73, the server seemed to assign the bit of 2^73 to 2^74 to another user immediately after the NF-PM1, then that TF assignment appeared to be performed with a CPU on Prime95 not mfaktc on GPU. See the screenshot below for details of M168086143. Attached Thumbnails   Last fiddled with by tuckerkao on 2021-10-21 at 23:20
2021-10-22, 01:56   #347
slandrum

Jan 2021
California

22·3·19 Posts

Quote:
 Originally Posted by tuckerkao After Dobri finished P-1 on an exponent with only TF up to 2^73, the server seemed to assign the bit of 2^73 to 2^74 to another user immediately after the NF-PM1, then that TF assignment appeared to be performed with a CPU on Prime95 not mfaktc on GPU.
So?

2021-10-26, 10:06   #348
tuckerkao

"Tucker Kao"
Jan 2020

2×251 Posts

Quote:
 Originally Posted by drkirkby If you want to find a prime number, there seems to me only two sensible places worth consideration. The smallest exponents you can get, that have not had a LL or PRP test, as those have both the highest probability of being producing a Mersenne prime, and also take the shortest period of time to test. Exponents somewhat over 332,000,000 which will yield at least 100,000,000 decimal digits, so nett one $50,000. Having tested one of them, M332646233, I concluded it was too much work. But at least I can see a point in why people do that. Your testing exponents around 168 million has several disadvantages. If the Mersenne number happens to be prime, the number of decimal digits is insufficient to get you the$50,000 prize. All you will get is \$3,000. The exponent is unlikely to be trial-factored sufficiently high, so you need to do the trial-factoring, so it takes extra time. The exponent is unlikely to have any P-1 factoring, so you need to do that, so it takes extra time. The exponent is less likely to yield a Mersenne prime than an exponent around 105.5 million, as it's generally believed the spacing between Mersenne primes increases with the exponent. The exponent is going to take around (168/105.5)2.1=2.54x as long to test To me at least, there's no reason to test around 168 million now.
There are only 7 exponents left without the PRP or LL results for M105M. 700 exponents remain for M106M. Very unlikely to find the hidden Mersenne Prime in your sensible range. I'll wait until Nov 9, 2021 to have the final say.
Attached Thumbnails

2021-10-27, 02:57   #349
LaurV
Romulan Interpreter

"name field"
Jun 2011
Thailand

100110010010012 Posts

Quote:
 Originally Posted by tuckerkao The numbers with the double double patterns are sometimes lucky, I only hope 1 of the results can be P-PRP for the co-factors.
You have to try working that out. You never know.

Fun story: I wanted for a very long time to test all exponents with 666 in them, but never moved my ass to really do it. This was BEFORE discovering of M45 (in fact, before M47, which was discovered first) and if I would have done it, I would be now famous and 50 thousand bucks richer.

So, if you really believe in your own forecast, move your butt and do those tests, and don't expect other people to do it for you.

Last fiddled with by LaurV on 2021-10-27 at 09:22

 2021-10-27, 08:33 #350 Zhangrc   "University student" May 2021 Beijing, China 2×5×11 Posts At least there's one special thing about 168 that has mathematical significance: The simple group of order 168, PSL(2,Z/7Z), is the second smallest non-trivial simple group.

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