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Old 2016-04-12, 10:05   #111
Sergei Chernykh
 
Jun 2015
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Quote:
Originally Posted by R. Gerbicz View Post
Are there any problems with the database?? When trying to download the large c2 files, say the 120 digits, then c2_120_1.txt and c2_120_2.txt is empty, c2_120_3.txt looks like good (its size is 252 MB), here killed the download. Similar problem for 110 digits: c2_110_1.txt and c2_110_2.txt is empty.

For me the download time was normal (3-4 minutes) for each of these files, so maybe only the generating part was broken?
This is apparently a common problem with large files: https://bugs.chromium.org/p/chromium...?id=138506#c26
File gets downloaded, but then the script hits Chrome's memory limit. Try downloading raw files from sech.me/ap/110/ as a workaround for now.
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Old 2016-04-12, 10:32   #112
R. Gerbicz
 
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"Robert Gerbicz"
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Quote:
Originally Posted by Sergei Chernykh View Post
This is apparently a common problem with large files: https://bugs.chromium.org/p/chromium...?id=138506#c26
File gets downloaded, but then the script hits Chrome's memory limit. Try downloading raw files from sech.me/ap/110/ as a workaround for now.
Thanks, that works.
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Old 2016-04-12, 14:54   #113
Sergei Chernykh
 
Jun 2015
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Quote:
Originally Posted by R. Gerbicz View Post
When trying to download the large c2 files, say the 120 digits, then c2_120_1.txt and c2_120_2.txt is empty, c2_120_3.txt looks like good (its size is 252 MB), here killed the download. Similar problem for 110 digits: c2_110_1.txt and c2_110_2.txt is empty.
This should be fixed now. I had to add server-side splitting of very large individual files when downloading, but it's a very simple and straight-forward PHP script, so it should never time out.
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Old 2016-05-10, 09:39   #114
Sergei Chernykh
 
Jun 2015
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I've posted a new article describing in details how we got to 1,000,000,000 known amicable pairs, thousands new type (i, 1) pairs and the first type (8, 1) pair: http://sech.me/ap/articles.html#a3

Last fiddled with by Sergei Chernykh on 2016-05-10 at 09:40
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Old 2016-08-16, 08:18   #115
Sergei Chernykh
 
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The search for all amicable pairs up to 1018 is completed!
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Old 2016-08-16, 10:27   #116
garambois
 
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Congratulations !
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Old 2016-08-16, 11:31   #117
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Well done getting 18 digits finished, I thought it would have taken much longer!

Do you have anything in place for adding any of the isotopic substitutions? Jan
use to add these when his database was running but I no longer have the list he sent me.
If anyone has a large list of breeders it should be easy to generate lots of these,
sort a list of (a*u,a) breeders
by u value, any time the u value is the same for different breeders the a values will form substitutions.

Eg. From the small list I have the first such pairs are
a=1485, u=3349 and a=9009,u=3349
meaning 1485=3^3*5*11 and 9009=3^2*7*11*13 are a substitution.
Note sigma(1485)/1485=sigma(9009)/9009=64/33 as required.

There is an example given in the Garcia et al 2003 survey paper and elsewhere
with seven numbers having the same sigma(x)/x value!

The fairest way of handling these would probably be to start from smaller numbers and work upwards, giving the credit to whoever found the original pair.
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Old 2016-08-16, 12:32   #118
Sergei Chernykh
 
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I've optimized my program even further, plus I used a trick from David Einstein to skip many large prime factors:

- Find all pairs of the form (a*p, b*q) where a and b <= 2*1011
- Find all pairs of the form (a*pk1, b*qk2) where k1 or k2 > 1

These two steps are quick, they took 4 days in total.

- All remaining pairs are of the form (a*p, b*q) where either a or b > 2*1011
- For p > 5*106 it means that b > 2*1011 and q < 107
- Many huge primes have a prime factor of sigma(p) that cannot occur as a factor of sigma(qk) for any prime q < 107, qk < 2*1018

This speeded up the search: it would have taken at least 6 months otherwise.

I have a list of isotopic relations from Jan, extended my findings. All isotopic pairs are already in.
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Old 2016-08-16, 17:28   #119
RenYuanhua
 
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Congratulations ! I found that no change in 18 in the homepage of AP days ago, the time completed search will come. great !!
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Old 2016-09-02, 13:19   #120
Sergei Chernykh
 
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I've run a filter on the entire amicable database to find pairs which were not generated by Borho/te Riele/Wiethaus rules, i.e. pairs which are not type (3+,2). There are just a bit more than 2 million such known pairs in total, so they are more interesting/unique in this sense. I've packed them in a separate archive, if anyone is interested: http://sech.me/ap/compressed/c2_filtered.7z
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Old 2016-09-05, 11:20   #121
AndrewWalker
 
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Hi Sergei if you could send me Jan's list please I'll have a go at updating my search to
check for them on the go. I'm mainly searching lower values with the BDE method at the
moment, finding quite a lot of pairs but unfortunately for some inputs a very high
percentage are already known!

Andrew
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