Twin prime list extended to k < 1M for n <= 15K
 

I have posted an updated twin prime list for k < 1M for 10K < n <= 15K in the 'Twin Prime Search' forum.

I did not do searches for twins for 100K < k < 1M for n <= 10K. There are just too many of them to post in a thread in one place. I've already searched all of my large k for twins and will post them closer to when Karsten gets back.

I'm currently sieving for twins up to n <= 20K for k < 1M.


Gary

Correction on my corrections :-)
 

[quote=gd_barnes;112543]4. k=65581096558109 should show as k=6558109. Note that it is in the correct sequence for k=6558109. (I thought this repeated value was kind of funny. It'd be interesting to actually test k=65581096558109.) :grin:Gary[/quote]


Oops. I should have stated:
k=6558109165581091 should show as k=65581091. Note that it is in the correct sequence for k=65581091.

(Missing a '1') Ergh! :rolleyes:


Gary

It turns out that I have overestimated my system performance, and I will be ready with 100001<k<199999 nmax=5000 till tomorrow. After that I will be out for vacations till 2-nd of September. If anyone want's to have a look at preliminary data for n<5000, I can upload it (2-3MB after compression) - just give me directions where (15k.org?).
BTW: I will complete it till n=20000 eventually, but it will take me more time than I have previously thought. I may also provide some interim data at e.g. 10k, 15k etc.
Karsten and Kosmaj - what do you think about it?

Calculation time testing across large ranges of k
 

[quote=Cruelty;112817] It turns out that I have overestimated my system performance, and I will be ready with 100001<k<199999 nmax=5000 till tomorrow.
[/quote]

Testing a range of 100,000 k is very large, even only testing up to n=10K. I only took a range of 9,000 k (k=1K to 10K) to n=10K and I seem to recall it taking 1-2 days to sieve and LLR on one core. So it's doable but I'm thinking it'll take you anywhere from 1 to 3 weeks to get to n=10K on one core running 24/7 on today's high-speed machines (i.e. 100,000/9,000 x 1-2 days). But if you're going to go to n=20K, watch out! Curtis may be able to calculate this more accurately than me, but I believe it will take you 6 to 9 times as long for LLRing vs. going to n=10K! :surprised This is because LLR time increases by the square of n. Here's how I came up with that:

The avg. n from n=1 to 10K = 5K.
The avg. n from n=10K to 20K = 15K.
(15K / 5K) ^ 2 = 9; hence 9 times longer.

Since Curtis has suggested using the 70% point (i.e. square root of 0.5) as a good point to determine how far to sieve, I'm thinking that it might be relavent here. So here is an estimate based on that:
70% point of n=1 to 10K = 7K
70% point of n=10K to 20K = 17K
(17K / 7K) ^ 2 =~ 5.9; hence about 6 times longer.

At low ranges of n like this, I don't think that these calculations are particularly accurate but if we were comparing testing the range of n=25K to 50K vs. testing n=50K to 75K, I'm sure it would be close to accurate. Regardless, I think it is still a good ballpark estimate.

Of course the sieving time increase is essentially inconsequential compared to the increase in LLR time for the two ranges of n.


Based on this, my suggestion is one of the two following:

1. If you only have 1-2 cores to dedicate to the effort...do BOTH 10K < k < 100K AND 100K < k < 200K up to n=10K first. This may take a total of 3-4 weeks of CPU time for sieving and LLRing. Then slowly work your way on both up to n=15K. You may want to stop there at that point but if not, going in baby steps, maybe n=2K at a time may be the way to go.

2. If you have 3 or more cores to dedicate to it, try putting them all on it and do your 100k < k < 200K to n=15K first. Then do the 10K < k < 100K to n=15K next. And then finish it up by extending both to n=20K. On 1 core, I think it would take you 6 months or more so to make it a manageable-sized project, you definitely want at least 3 cores on it.

Hope this helps...


Gary

Datos vs Gatos...
 

[quote=em99010pepe;112737]"Gatos" is cats in portuguese and in spanish......nothing to do with "new data page". Keep trying....[/quote]

Actually, it was "Datos" not "Gatos". See your original post about the topic. I googled "Datos Spanish translation" and it indeed is the Spanish translation of "Data".

Fortunately, they're all back to English. Like Cruelty said, I think someone was very bored!


G

back in town
 

hi all,
so my vacation is over and the real life is coming back i read not yet all new posts here but most of them.

to Gary: i corrected your twins found in post #49 here. that's all for me done now.
congrats for your first Top5000 candidate! (so work for me to update the contributors page :grin:)

it is correct that i have not yet marked all twins on the summary pages but it's the next work after bringing all pages upto-date. then i saw there're more efforts for twin-search for higher k's and n's so i can include them next too.
more work needs the page with remaining k's but it's of low priority.
karsten

Karsten

Welcome back!
There were two more posts about your latest update by Gary which I just moved to this thread, see above posts 63 and 67.

BTW, when I saw the new (now removed) title of this thread it was "gatos" not "datos" :smile: but that episode from a summer night's dream is now over :w00t:

corrections
 

Kosmaj:
i corrected all topics from the posts from gary (#63 and #67 too). thanks his eagle eyes!
the testrange for k=735 is correct: at PrimeSearch there're some uncompleted ranges but i found 4 more primes in Top 5000 so i included them (they were found in May and August 2006).
don't call me Mr. Micr*S*ft II please, but seems to be a right name: every new update there are new errors :grin:
Karsten

[quote=kar_bon;112970]Kosmaj:
i corrected all topics from the posts from gary (#63 and #67 too). thanks his eagle eyes!
the testrange for k=735 is correct: at PrimeSearch there're some uncompleted ranges but i found 4 more primes in Top 5000 so i included them (they were found in May and August 2006).
don't call me Mr. Micr*S*ft II please, but seems to be a right name: every new update there are new errors :grin:
Karsten[/quote]


Great to have you back Karsten! I hope you had a nice vacation. Where did you go?

I assume you saw the 14 omissions/corrections that I just posted in the last 2 hours to the 'double checking' thread. It includes 1 omission and 1 correction for primes found by others on a k that I currently have reserved. THAT effort was much more than the small stuff that I found in this thread. I'm sure that almost all of it was Prime Search errors and omissions.

I've held off on a couple of things until you got back but they aren't too big. I just have all the primes for k=26565 and 49335 up to n=150K to fill gaps on previously partially tested k's that I am keeping reserved for testing up to n=400K. I'll post those in the 'post small primes' thread in a little while. I also have twins for all 16 of my k's plus 4-5 more k's that I had searched a while back. I'll post those in this thread. Both will be quick efforts on your part.


Gary

Suggest follow up with Cruelty...
 

Kosmaj and/or Karsten,

IMPORTANT note: One or both of you might want to follow up with Cruelty on him testing the range of k=100K to k=200K up to n=5K (and maybe 10K or 20K) and posting primes for it later on. See his note earlier in this thread. This would be a lot of effort on your part and a lot of space needed by the 15k site, perhaps even 5 to 10 times more then my effort from k=1K to n=10K.

Just figured I better give you a heads up in case you missed it in the thread here.


Gary

Twins on all of my k's plus a few more
 

Karsten,

Attached are the twins on all of my 16 reserved k's plus several more and how far they have been tested. On one or two of these, you might have already shown them. There are a total of 62 twins in the list. One is for n=2932; a rare find when searching for twins by k. Also fairly rare for such a small list of k's is that one k has 8 twins and another k has 7 twins. The most I've found so far for one k is 10. I think Robert has found as many as 13.


Gary