20121027, 13:04  #133  
Romulan Interpreter
"name field"
Jun 2011
Thailand
2×11×449 Posts 
Quote:
I am still TFing the smaller MMs (raising the water marks). I will post numbers when I reach the computer tomorrow or on Monday. 

20130227, 08:44  #134 
Banned
"Luigi"
Aug 2002
Team Italia
2×41×59 Posts 
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 20130227 at 08:57 Reason: The project is open to your help! 
20130903, 05:52  #135 
"Åke Tilander"
Apr 2011
Sandviken, Sweden
1000110110_{2} Posts 
Largest prime of form 2*k*Mp+1 known?
You could say that the Deep sievingproject 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 sievingproject.
Last fiddled with by aketilander on 20130903 at 05:59 
20130903, 06:02  #136 
Romulan Interpreter
"name field"
Jun 2011
Thailand
2696_{16} Posts 
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<<p1; 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<<p1; 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 20130903 at 06:16 
20130903, 06:12  #137 
"Åke Tilander"
Apr 2011
Sandviken, Sweden
2×283 Posts 
My guess is that the largest known would be for M132049 or M216091?
Last fiddled with by aketilander on 20130903 at 06:13 
20130903, 06:36  #138 
"Åke Tilander"
Apr 2011
Sandviken, Sweden
1000110110_{2} Posts 
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. 
20130903, 06:44  #139  
Romulan Interpreter
"name field"
Jun 2011
Thailand
2×11×449 Posts 
Quote:
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 20130903 at 06:47 

20130903, 06:57  #140 
"Åke Tilander"
Apr 2011
Sandviken, Sweden
236_{16} Posts 
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. 
20130903, 07:45  #141 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
2^{5}·3·101 Posts 
30690*(2^1320491) + 1 is prime 148536*(2^1320491) + 1 is prime 185056*(2^1320491) + 1 is prime
by Tony Forbes via Will Edgington 
20130903, 10:51  #142  
Banned
"Luigi"
Aug 2002
Team Italia
2·41·59 Posts 
Quote:
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 

20130903, 11:40  #143  
"Åke Tilander"
Apr 2011
Sandviken, Sweden
2·283 Posts 
Quote:
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 20130903 at 11:47 

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