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 2011-01-20, 16:33 #34 Mini-Geek Account Deleted     "Tim Sorbera" Aug 2006 San Antonio, TX USA 102538 Posts I've started testing for twins (PRP or provable) of all primes on the top 5000 list that do not have a base of 2 (since I can test those by downloading Karsten's lists). The timestamp for the list was "Thu Jan 20 04:51:06 CST 2011". I made a Python script to parse it out, which I'll post when I have results to post. Due to the vastly varying bases, GFNs, Phi's, and factorials/primorials, I don't see how I can really presieve this efficiently, so I'm just running it in PFGW with -f.
 2011-01-21, 09:03 #35 gd_barnes     May 2007 Kansas; USA 2·5·1,013 Posts An excellent and very interesting work Tim. Nice job!
 2011-01-21, 09:28 #36 gd_barnes     May 2007 Kansas; USA 1013010 Posts David, Just to be clear: Do you plan to primality prove 5789*2^15513+3 ? Tim, I updated the status in post 32 to reflect what has now been done. Gary
2011-01-23, 17:00   #37
Mini-Geek
Account Deleted

"Tim Sorbera"
Aug 2006
San Antonio, TX USA

17·251 Posts

Quote:
 Originally Posted by Mini-Geek I've started testing for twins (PRP or provable) of all primes on the top 5000 list that do not have a base of 2 (since I can test those by downloading Karsten's lists). The timestamp for the list was "Thu Jan 20 04:51:06 CST 2011". I made a Python script to parse it out, which I'll post when I have results to post. Due to the vastly varying bases, GFNs, Phi's, and factorials/primorials, I don't see how I can really presieve this efficiently, so I'm just running it in PFGW with -f.
Results and Python 3.x parsing script attached. I also searched for twins of Proth primes (k*2^n+1) with a k over 10000 since those aren't on Karsten's list yet, and presieved that with srsieve. No primes found. Not counting numbers divisible by 3, I factored or tested 566 numbers. The other ones were of the type that they should be included on one of Karsten's lists.
Attached Files
 top5ktwinsearch.zip (8.8 KB, 128 views)

Last fiddled with by Mini-Geek on 2011-01-23 at 17:07

2011-01-23, 17:43   #38
henryzz
Just call me Henry

"David"
Sep 2007
Cambridge (GMT)

32×17×37 Posts

Quote:
 Originally Posted by gd_barnes David, Just to be clear: Do you plan to primality prove 5789*2^15513+3 ? Tim, I updated the status in post 32 to reflect what has now been done. Gary
I will test it. It will take a while. I will try to use multicores. We are in no hurry otherwise I wouldn't do it. It will eventually get finished. This number is small enough for me to eventually finish but large enough that I feel the need to use multicores.

Last fiddled with by henryzz on 2011-01-23 at 17:46

 2011-01-24, 19:39 #39 henryzz Just call me Henry     "David" Sep 2007 Cambridge (GMT) 32·17·37 Posts It will be about 100 hours of processing for phase 1. 4% done now. Begining to think multithreading is a waste of time for this small a number. I am running 2 threads and thread one has had 5/6 of the successes so far.
2011-01-24, 19:52   #40
Mini-Geek
Account Deleted

"Tim Sorbera"
Aug 2006
San Antonio, TX USA

17·251 Posts

Quote:
 Originally Posted by Mini-Geek Results and Python 3.x parsing script attached.
I've updated the script to handle extra-long/multi-line lines correctly. It can now read the entire current top 5000 list without any errors or placing numbers in the "confused" file (at least, from rank 1 to 5000 - not sure what'll happen if it sees all the other things at the top and bottom). In case anyone's interested, I'm attaching the updated version here.
Attached Files
 top5kparse.zip (845 Bytes, 127 views)

Last fiddled with by Mini-Geek on 2011-01-24 at 19:52

2011-01-28, 20:15   #41
mart_r

Dec 2008
you know...around...

21516 Posts

Quote:
 Originally Posted by Mini-Geek I don't know if a record list exists for non +-1 twin prime, or (probably the same) a pair of twin primes/PRPs, where at least one is only known to be a PRP. Given the obscurity of that, I'd guess my 5789*2^15513+1, +3 pair have a good chance of being that.

(20431926447260679*4001#*(205881*4001#+1)+210)*(205881*4001#−1)/35 +5, +7 (5132 digits)

?

Last fiddled with by mart_r on 2011-01-28 at 20:16

2011-01-28, 21:58   #42
Mini-Geek
Account Deleted

"Tim Sorbera"
Aug 2006
San Antonio, TX USA

17·251 Posts

Quote:
 Originally Posted by mart_r Uhm... What about the twin (20431926447260679*4001#*(205881*4001#+1)+210)*(205881*4001#−1)/35 +5, +7 (5132 digits) ?
I was not aware of these twin primes. Is the pair listed on a list anywhere, or did you just find the pair, or what? A google search can't find it, and it's not large enough to be on any list I can see. I can confirm with PFGW that they are primes. (the number between the primes is easily trial factored to at least 33.34%)
What about narrowing the definition to twins where at least one of the pair would (at time of discovery) best be proved by general methods like ECPP, (e.g. no N-1, N+1, or N-1/N+1 combined test is useful) whether they have been proven or are still PRP? Maybe it qualifies for that record! If not, I give up and admit it's not a terribly interesting twin, it just happens to be the largest I found in my search.

Last fiddled with by Mini-Geek on 2011-01-28 at 22:04

2011-01-29, 00:18   #43
davar55

May 2004
New York City

3×1,409 Posts

Quote:
 Originally Posted by Mini-Geek Code: 1381*2^6512+3 and below Mini-Geek (done, certificates in DB) 7027*2^13017-3 [unreserved] 755*2^13474-3 [unreserved] 5789*2^15513+3 henryzz Done PRPing all candidates and proving all candidates I said I would. All results I saved (started a little after n=20K) along with all primes in pfgw.log or pfgw-prime.log according to current proven status are attached. 2^13466917-3 would have taken a little over two days, but I put it on two cores for most of it, so it took closer to one day. Because it wasn't sieved very well, (only to 5 billion, or about 2^32) Prime95 chose P-1 bounds that gave it a 20% chance of finding a factor. Unfortunately it did not find a factor, even with such generous bounds, so I had to test it. Alas, the largest known twin Mersenne prime (i.e. 2^p-1 and (2^p-3 or 2^p+1) are prime) is just p=5: 29 and 31. Just for fun, here are all known primes that are twin Mersenne or Fermat primes: Code: 2^16+1, +3 (65537, 65539) 2^4+1, +3 (17, 19) 2^5-1, -3 (29, 31) 3, 5, and 7, by various formulas (3=2^1+1=2^2-1, 5=2^1+3=2^2+1=2^3-3, 7=2^2+3=2^3-1) I'd guess that such twin pairs are finite and fully listed there, even if there are infinite Mersenne, Fermat, and twin primes. AFAICT from a quick googling, the last time someone looked for Mersenne Twin Primes was in 1999, when the highest p known to make 2^p-1 prime was 3021377.
So has anyone factored

Quote:
 As you can see, there are only two numbers (2^4253-3 and 2^11213-3) in the table that I have not been able to factor.
either M(4253)-2 or M(11213)-2 since then?

2011-01-29, 03:30   #44
Mini-Geek
Account Deleted

"Tim Sorbera"
Aug 2006
San Antonio, TX USA

17·251 Posts

Quote:
 Originally Posted by davar55 So has anyone factored either M(4253)-2 or M(11213)-2 since then?
Not as far as I know, but I don't know of any serious ECM attempts, just that old TF to 2^32. Here are the FactorDB entries for those:
http://factordb.com/index.php?query=2^4253-3
http://factordb.com/index.php?query=2^11213-3

Last fiddled with by Mini-Geek on 2011-01-29 at 03:31

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