20210627, 19:10  #1200  
"Ed Hall"
Dec 2009
Adirondack Mtns
2^{4}×257 Posts 
Quote:


20210628, 12:34  #1201 
Aug 2020
79*6581e4;3*2539e3
3^{2}×47 Posts 
I used your software, it detected the merge of open ended 53^10, but not for the terminating 53^30. Is it supposed to be like that?
Btw, does factordb detect merges? That would be quite a useful feature. 
20210628, 12:55  #1202  
"Ed Hall"
Dec 2009
Adirondack Mtns
10020_{8} Posts 
Quote:
factordb only works directly with composites and factors. It does track merges in a manner, but that info is only available if you look for it. On a page for the first value that exists in both merged sequences, look at the "More information" section. Under the "Others:" block you will see previous terms that lead to the current one. If you follow those back up their sequences, you will arrive at the source sequences. I have used that method to find merges outside the 3*10^6 listing of C80s. 

20210628, 18:18  #1203 
Aug 2020
79*6581e4;3*2539e3
3^{2}·47 Posts 
I tried going along the "More information" path, but figured it might take very long with uncertain outcome.
I noticed that for prime b: s(b^n) = (b^n1)/(b1). It's probably well known and even I realized it's simply because s(b^n) = 1 + b^1 + b^2 + ... b^(n2) + b^(n1) is a geometric series, but I was wondering if that doesn't mean that if b and n satisfy b^n = (b^n  1) / (b1), then b^n is a perfect number? I'm not sure though if that equation even has solutions. Last fiddled with by bur on 20210628 at 18:19 
20210629, 00:31  #1204  
"Alexander"
Nov 2008
The Alamo City
2^{3}×97 Posts 
Quote:


20210630, 12:39  #1205 
Aug 2020
79*6581e4;3*2539e3
110100111_{2} Posts 
Happy, too bad, but it'd been a surprise if there was an integer solution.
Quick update on the 53 base, I ran all n <= 100 to a cofactor of at least 105 digits. Now I'm trying to terminate all the trivial sequences that were too large for factordb to take care of them, starting with n = 69. There are quite a few cofactors larger than 150 digits, so it might take some time. 
20210630, 14:13  #1206  
"Garambois JeanLuc"
Oct 2011
France
1255_{8} Posts 
Quote:
But indeed, it should take some time. Thank you very much for all this work ! I will add the 53 base to the next update. 

20210630, 19:16  #1207 
Aug 2020
79*6581e4;3*2539e3
647_{8} Posts 
Yes, they decrease relatively fast, there was even a semiprime once, that caused a tremendous drop in size.
But no need to thank me, I could as well thank you for organizing it. And if some of the larger ones really withstand ECM they could at least be used to help vbcurtis optimize his cado parameters. 
20210701, 17:38  #1208 
Aug 2020
79*6581e4;3*2539e3
423_{10} Posts 

20210701, 23:12  #1209  
"Alexander"
Nov 2008
The Alamo City
2^{3}×97 Posts 
Quote:
 Base 48 is done. I got to i=80 on the trivial sequences (135 digits). Base 24 is also done to i=50. If nobody reserves the priority cycle bases by the time I finish my catchup with GIMPS, I may take one or both of those. 

20210702, 17:27  #1210  
"Garambois JeanLuc"
Oct 2011
France
5·137 Posts 
Quote:
I will add the base 48 in the next update. 

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