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Old 2011-01-20, 16:33   #34
Mini-Geek
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"Tim Sorbera"
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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.
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Old 2011-01-21, 09:03   #35
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An excellent and very interesting work Tim. Nice job!
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Old 2011-01-21, 09:28   #36
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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
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Old 2011-01-23, 17:00   #37
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Quote:
Originally Posted by Mini-Geek View Post
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
File Type: zip top5ktwinsearch.zip (8.8 KB, 127 views)

Last fiddled with by Mini-Geek on 2011-01-23 at 17:07
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Old 2011-01-23, 17:43   #38
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Quote:
Originally Posted by gd_barnes View Post
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
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Old 2011-01-24, 19:39   #39
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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.
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Old 2011-01-24, 19:52   #40
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Quote:
Originally Posted by Mini-Geek View Post
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.
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File Type: zip top5kparse.zip (845 Bytes, 126 views)

Last fiddled with by Mini-Geek on 2011-01-24 at 19:52
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Old 2011-01-28, 20:15   #41
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Quote:
Originally Posted by Mini-Geek View Post
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.
Uhm... What about the twin

(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
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Old 2011-01-28, 21:58   #42
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Quote:
Originally Posted by mart_r View Post
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
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Old 2011-01-29, 00:18   #43
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Quote:
Originally Posted by Mini-Geek View Post
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?
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Old 2011-01-29, 03:30   #44
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Quote:
Originally Posted by davar55 View Post
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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