20150111, 19:54  #45 
"Ed Hall"
Dec 2009
Adirondack Mtns
2·1,607 Posts 
Latest Find:
Code:
28405878617032 = 2E3.7.17.317.94126523 36247748188088 = 2E3.23.131.1503806347 35213129468872 = 2E3.53.191.2417.179899 32437790595128 = 2E3.3391.14747.81083 I was unaware there may be undiscovered amicable pairs within the regions we're examining. I also am not sure if I still have all of the ones I've found, since I've been concentrating on 4 cycle and (although there shouldn't be any), I occasionally check to see if any 3 cycles turned up. The only amicable work I had been doing was using the known lists on occasion to validate changes in my code, but since I've started finding 4 cycles, I now use those. Maybe I'll toss something together to do a check on what I may have against the lists... 
20150111, 21:05  #46 
Nov 2011
233 Posts 
Ed, as far as I know, the exhaustive search of amicable pairs has been made up to 10^14. So in the range you are working with there should not be any new undiscovered amicable pairs.
By the way, congratulations with all your last findings! 
20150112, 21:09  #47  
Nov 2011
E9_{16} Posts 
Quite unexpectedly a program have found a new cycle:
Quote:


20150112, 21:58  #48 
"Serge"
Mar 2008
Phi(3,3^1118781+1)/3
9055_{10} Posts 

20150113, 00:32  #49 
"Ed Hall"
Dec 2009
Adirondack Mtns
110010001110_{2} Posts 

20150308, 10:56  #50  
Mar 2015
Australia
2·41 Posts 
Quote:
Just this year I've started looking in the 15, 16 digit range again. To confirm what was mentioned above David finished the 14 digit amicables. From the numbers on Jans old page it looks like the 15d is probably over 90% done. I hope we can get you pairs and any other new ones incorporated into the lists! Andrew 

20150309, 09:56  #51  
Nov 2011
233 Posts 
Quote:
According to Pedersen's list that 16digit number were found by Walker (You?) and Enstein in 2001. I can confirm that it is the smallest (and in fact the only 16 digits) amicable pair coprime with 6. As one of the tests I searched for all such pairs up to 10^16 At the moment a search for odd aliquot cycles runs almost autonomously on one of my laptops. I just check it twice a week. It reached n up to 27e8 (with n defined in my previous post). At the moment 289 nonlisted pairs were found. I attach the file with all of them. No more longer cycles were discovered. As far as I can see you did the search for all 15digits pairs such that the largest prime divisor of the least term of the pair is at most 7 digits. At least all except one new discovered pairs have the biggest prime divisor of the smallest element bigger than 10 millions. And one exception is divisible by 3^11. It would be nice to join the efforts. With only my poor computer resources it will take probably half a year to finish the search of all odd 15 digits cycles. Dmitry Last fiddled with by Drdmitry on 20150309 at 09:56 

20150310, 22:50  #52 
Mar 2015
111_{2} Posts 
Welcome
I have new algorithm , to find all amicable numbers <10^15. I send my pairs to http://math.eku.edu/amicablepairsdownload. Dou you know people are looking for amicable numbers 10^15?? 
20150311, 09:10  #53 
Mar 2015
Australia
82_{10} Posts 
Hi Dmitry, that Walker is me. The search we did on the 15d was up to 10 million for the largest factor of the first number, it should be complete but if you find any missing let me know! Also did a little on the 16 digits but that was very far from complete.
I've just finished a run on 15d and 16d with factors up to 10000 for the first number. Again some are missed for the higher 16 digits because it is near the precision limit. I'm now starting a higher search for the even 15 digits. and will later do the same for the odds even if it's just a double check on yours. I've no idea what the highest possible factor for these is. Andrew 
20150311, 09:58  #54  
Nov 2011
233 Posts 
Quote:
Code:
166804820674965 = 3^11*5*11*41*211*1979 170487987977835 = 3^5*5*11*149*461*185711 I guess, you only search for amicable pairs, no longer Aliquot cycles? 

20150311, 11:15  #55 
Mar 2015
Australia
2×41 Posts 
Interesting, I've got that written down as the very last of the odd pairs found, so it may have been
cut off accidentally before being sent in. From my latest run for 16d 5903755662561705=3^11.5.13^2.29.311.4373 6041108390596695=3^11.5.13^2.89.467.971 5480828320492525=5^2.7^2.11.13.17.19.23.31.103.1319 5786392931193875=5^3.7.11.13.19.31.37.43.61.809 were the final two found. I'm only searching for pairs. I'll try and get in touch with a few people from a while back next week. Andrew 
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