20160412, 10:05  #111  
Jun 2015
Stockholm, Sweden
83 Posts 
Quote:
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. 

20160412, 10:32  #112  
"Robert Gerbicz"
Oct 2005
Hungary
10101110111_{2} Posts 
Quote:


20160412, 14:54  #113 
Jun 2015
Stockholm, Sweden
83 Posts 
This should be fixed now. I had to add serverside splitting of very large individual files when downloading, but it's a very simple and straightforward PHP script, so it should never time out.

20160510, 09:39  #114 
Jun 2015
Stockholm, Sweden
83_{10} Posts 
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 20160510 at 09:40 
20160816, 10:27  #116 
Oct 2011
3×113 Posts 
Congratulations !

20160816, 11:31  #117 
Mar 2015
Australia
52_{16} Posts 
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. 
20160816, 12:32  #118 
Jun 2015
Stockholm, Sweden
83 Posts 
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*10^{11}  Find all pairs of the form (a*p^{k1}, b*q^{k2}) 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*10^{11}  For p > 5*10^{6} it means that b > 2*10^{11} and q < 10^{7}  Many huge primes have a prime factor of sigma(p) that cannot occur as a factor of sigma(q^{k}) for any prime q < 10^{7}, q^{k} < 2*10^{18} 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. 
20160816, 17:28  #119 
"Ren Yuanhua"
Oct 2015
Guangzhou,China
4_{10} Posts 
Congratulations ! I found that no change in 18 in the homepage of AP days ago, the time completed search will come. great !!

20160902, 13:19  #120 
Jun 2015
Stockholm, Sweden
83_{10} Posts 
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

20160905, 11:20  #121 
Mar 2015
Australia
2×41 Posts 
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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