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2012-10-27, 13:04   #133
LaurV
Romulan Interpreter

"name field"
Jun 2011
Thailand

2×11×449 Posts

Quote:
 Originally Posted by ET_ 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.

 2013-02-27, 08:44 #134 ET_ 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 2013-02-27 at 08:57 Reason: The project is open to your help!
 2013-09-03, 05:52 #135 aketilander     "Åke Tilander" Apr 2011 Sandviken, Sweden 10001101102 Posts 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
 2013-09-03, 06:02 #136 LaurV Romulan Interpreter     "name field" Jun 2011 Thailand 269616 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< p=521; m=1< Last fiddled with by LaurV on 2013-09-03 at 06:16
 2013-09-03, 06:12 #137 aketilander     "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 2013-09-03 at 06:13
2013-09-03, 06:36   #138
aketilander

"Åke Tilander"
Apr 2011
Sandviken, Sweden

10001101102 Posts

Quote:
 Originally Posted by LaurV 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.

2013-09-03, 06:44   #139
LaurV
Romulan Interpreter

"name field"
Jun 2011
Thailand

2×11×449 Posts

Quote:
 Originally Posted by aketilander 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

2013-09-03, 06:57   #140
aketilander

"Åke Tilander"
Apr 2011
Sandviken, Sweden

23616 Posts

Quote:
 Originally Posted by LaurV 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.

 2013-09-03, 07:45 #141 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 25·3·101 Posts 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
2013-09-03, 10:51   #142
ET_
Banned

"Luigi"
Aug 2002
Team Italia

2·41·59 Posts

Quote:
 Originally Posted by LaurV 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

2013-09-03, 11:40   #143
aketilander

"Åke Tilander"
Apr 2011
Sandviken, Sweden

2·283 Posts

Quote:
 Originally Posted by Batalov 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

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