20150813, 11:39  #23 
Mar 2015
Australia
1010010_{2} Posts 
Thanks for the update Sergei! If it's easy to work out it would be interesting to know
what the highest prime factor for the first number is for each digit range. It would also be interesting to know if any more not divisible by 2 or 3 turn up, after the 16d pair the next two are in the 19d file. Andrew Last fiddled with by AndrewWalker on 20150813 at 11:39 
20150814, 07:15  #24  
Jun 2015
Stockholm, Sweden
1010011_{2} Posts 
Quote:
c2_3.txt: 1 pairs, largest factor 11 c2_4.txt: 4 pairs, largest factor 251 c2_5.txt: 8 pairs, largest factor 137 c2_6.txt: 29 pairs, largest factor 2393 c2_7.txt: 66 pairs, largest factor 60659 c2_8.txt: 128 pairs, largest factor 539783 c2_9.txt: 350 pairs, largest factor 3041279 c2_10.txt: 841 pairs, largest factor 5118431 c2_11.txt: 1913 pairs, largest factor 141374879 c2_12.txt: 4302 pairs, largest factor 974705471 c2_13.txt: 9877 pairs, largest factor 18510661889 c2_14.txt: 21855 pairs, largest factor 152504187263 c2_15.txt: 47728 pairs, largest factor 895732991999 c2_16.txt: 87558 pairs, largest factor 7160665580639 c2_17.txt: 4873 pairs, largest factor 631052035696799 c2_18.txt: 4169 pairs, largest factor 319606267871249 c2_19.txt: 4290 pairs, largest factor 5254683154329599 c2_20.txt: 4742 pairs, largest factor 31159681634452799 c2_21.txt: 4859 pairs, largest factor 477095265966920831 c2_22.txt: 4701 pairs, largest factor 722471849465034239 

20150820, 13:10  #25 
Nov 2011
2·3^{2}·13 Posts 
At last the search of all 15d odd cycles is over. In total there are 6 such pairs.
The search of 16d odd cycles had been started on this forum a couple of months ago and is moving slowly. It did not find any 16d odd cycle yet. 
20150911, 12:25  #26 
Jun 2015
Stockholm, Sweden
83 Posts 
The search of amicable pairs up to 10^17 is almost finished (currently searching largest prime factors near 10^11). Now that I have more data than ever, I've tried to find a good approximation for A(x)  the number of amicable pairs with smaller member <= x. I know A(x) for x <= 10^16 and a very accurate estimate for x=10^17 based on pairs I found so far and pairs known before.
It can be clearly seen from the table below that A(x)=x^{1/(3+e(x))} where e(x)>0 as x>infinity. So I tried f(x)=x^{1/(3+1/ln(x))} and it seems to be a very good approximation Code:
x ln(x)/ln(A(x)) A(x) f(x) 10^4 5,722706232 5 19 10^5 4,488558588 13 41 10^6 3,696289926 42 89 10^7 3,442469864 108 193 10^8 3,371385028 236 416 10^9 3,251565357 586 896 10^10 3,170150901 1427 1930 10^11 3,121677483 3340 4159 10^12 3,090229261 7642 8960 10^13 3,063502173 17519 19302 10^14 3,046651059 39374 41582 10^15 3,036419958 87102 89579 10^16 3,030003782 190775 192979 10^17 3,025652216 ~415550 415737 
20150929, 20:38  #27 
Jun 2015
Stockholm, Sweden
83 Posts 
The search of all amicable pairs up to 10^17 completed today at 12:47:01 CEST. There are 415523 pairs with smaller member < 10^17, 224748 of them are 17digit. Started the search up to 10^18 and found over 20000 new 18digit pairs in first 10 hours One of those 18digit pairs is coprime to 6:
Code:
936789193264049125=5^3*7^2*11*13*17*19*23*47*67*131*349 1009532413277262875=5^3*7^2*11*13*17*19*79*659*68543 
20151001, 05:23  #28  
"Robert Gerbicz"
Oct 2005
Hungary
10101011000_{2} Posts 
Quote:
Returning to speed: With my new code I can find amicable pairs up to 1e13 in less than 8 hours on a single(!) Corei32350M (2.30 GHz), so faster than your program's time previously posted (25 core hours on Core i74770K). It is a c++ code, what it still needs to make a parallel version of this (but that would not be hard with OpenMp, that is available on gcc). We could do a distributed search, but as my program is rather long and the complexity isn't that obvious first test it for smaller limits (say for limit=10^n for n<=16) to see the speed of the code. ps. I would advice to submit the pairs to Patrick. 

20151001, 05:36  #29  
Jun 2015
Stockholm, Sweden
83_{10} Posts 
Quote:
Last fiddled with by Sergei Chernykh on 20151001 at 06:35 

20151001, 08:35  #30  
Mar 2015
Australia
122_{8} Posts 
Quote:
to make life easier. Processing them with the existing software looks to be time consuming, he said it was only designed for small updates. I'm also in the position of having older pairs still to submit but I'm not going to flood him with them. Jan used to be able to take larger submissions, perhaps someone on the board with decent programing experience could offer to help out? (Pat did mention the program was written by someone who was close to retiring so obviously having enough spare time is one factor) Andrew 

20151001, 08:44  #31 
Jun 2015
Stockholm, Sweden
83 Posts 
I can at least have a look at his programs and estimate the work needed. Even rewriting it from scratch would take a week max. It's just a database, submission form, download form and a verification program.
Last fiddled with by Sergei Chernykh on 20151001 at 08:49 
20151002, 21:28  #32  
Nov 2011
2·3^{2}·13 Posts 
Quote:
By the way, Sergei, maybe you should email Pat and ask him about your submission? He processed my one month old submission which seems to be made later than yours. 

20151002, 21:37  #33  
Jun 2015
Stockholm, Sweden
83 Posts 
Quote:


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