mersenneforum.org  

Go Back   mersenneforum.org > Factoring Projects > Operazione Doppi Mersennes

Reply
 
Thread Tools
Old 2012-10-27, 13:04   #133
LaurV
Romulan Interpreter
 
LaurV's Avatar
 
"name field"
Jun 2011
Thailand

2×11×449 Posts
Default

Quote:
Originally Posted by ET_ View Post
BTW, is anybody else testing/sieving? I had MM(1257787), k=93 reserved by LaurV...
Finished long ago, but as I said I am still in holiday (19-28) and did not hurry to report it. The corespondent q for k=93 is not a factor of that MM. The next candidate is k=113 (not testing it, sieved to 20G). So you can safely say in the history table that k=112 is the watermark.

I am still TF-ing the smaller MMs (raising the water marks). I will post numbers when I reach the computer tomorrow or on Monday.
LaurV is offline   Reply With Quote
Old 2013-02-27, 08:44   #134
ET_
Banned
 
ET_'s Avatar
 
"Luigi"
Aug 2002
Team Italia

2×41×59 Posts
Cool Some updates...

For those interested in searching very big primes, I started using pfgw on our project deep sieving.

I can test compositeness of possible factors Q=2*k*(Mp)+1 of MMp for MM(34), MM(35), MM(36), MM(37) and MM(38). The timing of each test ranges from 1 hour to 2 days average.

Note also that the top limit of factoring has been raised to 30T (and up) for the bigger double Mersennes, while it is blocked to 800G for MM(34) and MM(35), and to 1.5T for MM(36) and MM(37). The factoring limit for MM(38) is 12T.

I am using a Pari/GP script from LaurV to check possible Ks, Ernst Mayer siever to deep sieving, and pfgw to primality check.
I finally wrote a slow GMP program to test MMp mod Q in case PFGW finds a PRP.

ATM I am checking numbers that range from 400,000 digitsd to 2,200,000 digits.

Luigi

P.S. You may contribute to this subproject. I'm working on a reservation page to maintain the status of the search. It is possible to:
1 - Extend the DB with more ks (PARI)
2 - Sieving (factor_qmmp)
3 - PRP testing (pfgw)

Last fiddled with by ET_ on 2013-02-27 at 08:57 Reason: The project is open to your help!
ET_ is offline   Reply With Quote
Old 2013-09-03, 05:52   #135
aketilander
 
aketilander's Avatar
 
"Åke Tilander"
Apr 2011
Sandviken, Sweden

10001101102 Posts
Default Largest prime of form 2*k*Mp+1 known?

You could say that the Deep sieving-project tries to find primes of the form 2*k*Mp+1 which possibly could be a factor of a MMp. For larger Mp:s it is very difficult to find primes of this form 2*k*Mp+1. Since the numbers are so large the probability of them being prime is very low of course. So my question is: Which is the largest known prime of this kind? (I mean independantly of being a factor or not of MMp of course). I did not find any at The list of the 5000 largest known primes. To the best of my knowledge there are none found yet within the Deep sieving-project.

Last fiddled with by aketilander on 2013-09-03 at 05:59
aketilander is offline   Reply With Quote
Old 2013-09-03, 06:02   #136
LaurV
Romulan Interpreter
 
LaurV's Avatar
 
"name field"
Jun 2011
Thailand

269616 Posts
Default

There are none known out of this list. For really BIG ones, the best way to prove their primality is to show that they divide some MMp (therefore the "regardless..." in your post is not necessary). The small ones which does not divide some MMp, many can be found, but they are not interesting. For the average one, like few million digits or so, we are still looking...

edit: (schoolgrade playing):
Code:
(13:10:38) gp > p=127; m=1<<p-1; for(k=1,1000,if(isprime(n=2*k*m+1),print(n" "k)))
19396094914493492417412352623610788052879 57
21097506749098184734729225660769629110149 62
66014779182662061911894673841763033022077 194
69417602851871446546528419916080715136617 204
84730309363313677402380277250510284652047 249
118418263688486585285254363386255337585993 348
125564193393826293017985230142322470026527 369
131689275998403185360325973076094297832699 387
132710123099166000750716096898389602467061 390
158911865352078262437395941670635754749019 467
166398077424338908633590183034134655401007 489
187835866540358031831782783302336052722609 552
196683208080302431881830523095562026220413 578
200086031749511816516464269169879708334953 588
206891679087930585785731761318515072564033 608
217440432462479678153096374148899887119107 639
232753138973921909008948231483329456634537 684
251808951521494462962897209499508476475961 740
268482787500620447672602565263665118837207 789
285837188213588309309234670242685297621361 840
288899729515876755480405041709571211524447 849
290941423717402386261185289354161820793171 855
296045659221216463213135908465638343964981 870
305233283128081801726647022866296085674239 897
307274977329607432507427270510886694942963 903
317143165970314647947865134126407973075129 932
331775307747915001876790242245974006167651 975
(13:10:51) gp > p=521; m=1<<p-1; for(k=1,1000,if(isprime(n=2*k*m+1),print(n" "k)))
2306572013803884864233918668491348121002530260848150617556539722286342509621612433513180039262248730472371560627537568300472987967904792321024873505814659202737 168
4366011311843067778728488908215766086183360850891142240374878760042005464640909249149947931460685096965560454044981825711609584367819785464797081993149176348037 318
5217246221699263383386244607301858845124770828108912111139792228981012819382218599613145326902705461782745196657525452108212710879784649297556261501247443434761 380
5848807606431279477164579480817347021113558875722096208804082867226082792254802956408420813843559280840656457305541691047627933775758580528313072104030028692653 426
7331603901019491175600670053418927956043756900553050177233286974410160119868696663666893696226433464715752460566101556383646283183697375591829062214910881037269 534
(13:11:08) gp >

Last fiddled with by LaurV on 2013-09-03 at 06:16
LaurV is offline   Reply With Quote
Old 2013-09-03, 06:12   #137
aketilander
 
aketilander's Avatar
 
"Åke Tilander"
Apr 2011
Sandviken, Sweden

2×283 Posts
Default

My guess is that the largest known would be for M132049 or M216091?

Last fiddled with by aketilander on 2013-09-03 at 06:13
aketilander is offline   Reply With Quote
Old 2013-09-03, 06:36   #138
aketilander
 
aketilander's Avatar
 
"Åke Tilander"
Apr 2011
Sandviken, Sweden

10001101102 Posts
Default

Quote:
Originally Posted by LaurV View Post
edit: (schoolgrade playing):
Yes for the small ones it is really easy, but very quickly it starts to get difficult.

For MM132049 has been sieved to k=244903 and out of probability reasons it would be strange if no primes or prp:s has been found. For MM216091 to k=123376 it is possible but probably not found any primes or prp:s. For larger Mp:s it is very unprobable I guess.
aketilander is offline   Reply With Quote
Old 2013-09-03, 06:44   #139
LaurV
Romulan Interpreter
 
LaurV's Avatar
 
"name field"
Jun 2011
Thailand

2×11×449 Posts
Default

Quote:
Originally Posted by aketilander View Post
For MM132049 has been sieved to k=244903 and out of probability reasons it would be strange if no primes or prp:s has been found. For MM216091 to k=123376 it is possible but probably not found any primes or prp:s. For larger Mp:s it is very unprobable I guess.
I think you got this wrong, that is only the "watermark". 244903 is the highest k which was tested and the number generated by this k (q=2kMx+1) did not divide MMx. This says nothing about the primality of the numbers q generated by lower k's. Because the divisibility is (MUCH) easier to test than the primality of q.

Now I see, in fact, the watermarks are much higher, I raised them a lot last year, but either I forgot report, or Et forgot to modify the tables... Hm... I don't see my name there...

Last fiddled with by LaurV on 2013-09-03 at 06:47
LaurV is offline   Reply With Quote
Old 2013-09-03, 06:57   #140
aketilander
 
aketilander's Avatar
 
"Åke Tilander"
Apr 2011
Sandviken, Sweden

23616 Posts
Default

Quote:
Originally Posted by LaurV View Post
I think you got this wrong.
Yes, I see now what you mean, of course we TF without doing any primality testing of possible factors. Sorry!

Even so, the question about "the largest known" still interests me even if this "largest" is very small. You have probably TFed MM132049 and MM216091 using at least some primes then even though you didn't know that they were primes.
aketilander is offline   Reply With Quote
Old 2013-09-03, 07:45   #141
Batalov
 
Batalov's Avatar
 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

25·3·101 Posts
Default

30690*(2^132049-1) + 1 is prime 148536*(2^132049-1) + 1 is prime 185056*(2^132049-1) + 1 is prime
by Tony Forbes via Will Edgington
Batalov is offline   Reply With Quote
Old 2013-09-03, 10:51   #142
ET_
Banned
 
ET_'s Avatar
 
"Luigi"
Aug 2002
Team Italia

2·41·59 Posts
Default

Quote:
Originally Posted by LaurV View Post
Now I see, in fact, the watermarks are much higher, I raised them a lot last year, but either I forgot report, or Et forgot to modify the tables... Hm... I don't see my name there...
Or you reported the results but ET_ didn't understand they were updates
Or you told me that it was still work in progress, and I kept waiting for more updates.

Please send me your results with a couple of lines that explain what to update, and I will.

Also, please share with me your ideas to advance the project: I will do my best to apply them.

Luigi
ET_ is offline   Reply With Quote
Old 2013-09-03, 11:40   #143
aketilander
 
aketilander's Avatar
 
"Åke Tilander"
Apr 2011
Sandviken, Sweden

2·283 Posts
Default

Quote:
Originally Posted by Batalov View Post
30690*(2^132049-1) + 1 is prime 148536*(2^132049-1) + 1 is prime 185056*(2^132049-1) + 1 is prime
by Tony Forbes via Will Edgington
Excellent Batalov, I had not seen that! Thank you!

Luigi, if we get the permission, it may be nice including this information at the Double Mersenne page also?

Last fiddled with by aketilander on 2013-09-03 at 11:47
aketilander is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
Is CEMPLLA 1.5 "the only software in the world capable of discovering" something? Not really. CRGreathouse Number Theory Discussion Group 51 2018-12-16 21:55
Official "World cup 2014/2018" teat LaurV Hobbies 74 2018-07-11 19:33
Problem E7 of Richard Guy's "Unsolved problems in number theory" Batalov Computer Science & Computational Number Theory 40 2013-03-16 09:19
Is the USA the "new" peacekeeper of the world?? outlnder Soap Box 20 2005-02-03 09:30
Would Minimizing "iterations between results file" may reveal "is not prime" earlier? nitai1999 Software 7 2004-08-26 18:12

All times are UTC. The time now is 21:51.


Fri Jan 28 21:51:12 UTC 2022 up 189 days, 16:20, 1 user, load averages: 2.43, 2.94, 3.35

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2022, 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.

≠ ± ∓ ÷ × · − √ ‰ ⊗ ⊕ ⊖ ⊘ ⊙ ≤ ≥ ≦ ≧ ≨ ≩ ≺ ≻ ≼ ≽ ⊏ ⊐ ⊑ ⊒ ² ³ °
∠ ∟ ° ≅ ~ ‖ ⟂ ⫛
≡ ≜ ≈ ∝ ∞ ≪ ≫ ⌊⌋ ⌈⌉ ∘ ∏ ∐ ∑ ∧ ∨ ∩ ∪ ⨀ ⊕ ⊗ 𝖕 𝖖 𝖗 ⊲ ⊳
∅ ∖ ∁ ↦ ↣ ∩ ∪ ⊆ ⊂ ⊄ ⊊ ⊇ ⊃ ⊅ ⊋ ⊖ ∈ ∉ ∋ ∌ ℕ ℤ ℚ ℝ ℂ ℵ ℶ ℷ ℸ 𝓟
¬ ∨ ∧ ⊕ → ← ⇒ ⇐ ⇔ ∀ ∃ ∄ ∴ ∵ ⊤ ⊥ ⊢ ⊨ ⫤ ⊣ … ⋯ ⋮ ⋰ ⋱
∫ ∬ ∭ ∮ ∯ ∰ ∇ ∆ δ ∂ ℱ ℒ ℓ
𝛢𝛼 𝛣𝛽 𝛤𝛾 𝛥𝛿 𝛦𝜀𝜖 𝛧𝜁 𝛨𝜂 𝛩𝜃𝜗 𝛪𝜄 𝛫𝜅 𝛬𝜆 𝛭𝜇 𝛮𝜈 𝛯𝜉 𝛰𝜊 𝛱𝜋 𝛲𝜌 𝛴𝜎 𝛵𝜏 𝛶𝜐 𝛷𝜙𝜑 𝛸𝜒 𝛹𝜓 𝛺𝜔