Sociable Numbers

[Drdmitry]

I have recently found a new 14d amicable cycle:

17348080951648 = 2^5*19*173*164930797
18811347201872 = 2^4*167*3719*1893029
17863761690928 = 2^4*53*419*50276269
17484478220672 = 2^7*260207*524957

By some strange reason it slipped from the EdH search.

Yes, I adapted my program to search for 14d even Aliquot cycles. I am not sure if I will make it a joint project. That will require more time for adjusting. Possibly during the summer vacations I will make programs for searching 17d odd and 15d even Aliquot cycles available.

[EdH]

Originally Posted by Drdmitry

I have recently found a new 14d amicable cycle:
...
By some strange reason it slipped from the EdH search.
...

Congratulations Drdmitry!

I just tested it with my program here and there should have been no reason for missing it. I will research more later to see why, but for now I don't have the machines that could shed any light running. I suppose I will wait until I can at least see which machine should have caught that one, rather than speculate now. It may be quite some time...

Good Searching!!

[Drdmitry]

Two new cycles are discovered:

69631368756488 = 2^3*7*11*463*4153*58787
93536879235832 = 2^3*6607*1769654897
81871314253928 = 2^3*53*71*2719615807
76736679668632 = 2^3*71*317*426182297

81539910932576 = 2^5*43*2399*24701399
82793562987424 = 2^5*23*61*73*163*154981
93525922343264 = 2^5*467*6258426281
90997518155224 = 2^3*89*127805503027

[R. Gerbicz]

I've submitted 1161 new sociable cycles to David Moews, now it is live on http://djm.cc/sociable.txt , with these "There are 1593 cycles in all". All of these cycles are using Borho's rule, among these 44 is irregular, the rest is regular. The new world record (in length) is:

1593   6565263345087801887264097577902586084802308668253459279997980655078178893197196   2E2.13.17.61.2267.649457.29999794873631769808793599.2756448252069968237497066556396168024959
       6756217977479959847564696756091232439215324480330666571194710499340853629554804   2E2.13.17.61.2267.649457.85098054346078731543403789430398550817570610130234131889664754559
       6952726640185205961345987236235112492919118210834800083930960631006604946296716   2E2.17.23.83.131.898727869067759.30872292268301465296606493.14735739372308374787788127219519
       6756217977479959847564696756092162758638061537516410401034202981400869121568884   2E2.17.23.83.131.898727869067759.442068232318120098775357451939111659069166143819457690333

with 79 digits.

[Drdmitry]

Originally Posted by R. Gerbicz

I've submitted 1161 new sociable cycles to David Moews, now it is live on http://djm.cc/sociable.txt , with these "There are 1593 cycles in all". All of these cycles are using Borho's rule, among these 44 is irregular, the rest is regular. The new world record (in length) is:

1593   6565263345087801887264097577902586084802308668253459279997980655078178893197196   2E2.13.17.61.2267.649457.29999794873631769808793599.2756448252069968237497066556396168024959
       6756217977479959847564696756091232439215324480330666571194710499340853629554804   2E2.13.17.61.2267.649457.85098054346078731543403789430398550817570610130234131889664754559
       6952726640185205961345987236235112492919118210834800083930960631006604946296716   2E2.17.23.83.131.898727869067759.30872292268301465296606493.14735739372308374787788127219519
       6756217977479959847564696756092162758638061537516410401034202981400869121568884   2E2.17.23.83.131.898727869067759.442068232318120098775357451939111659069166143819457690333

with 79 digits.

That is impressive!

[R. Gerbicz]

Originally Posted by Drdmitry

That is impressive!

Thanks! It was really a massive submission. The previous world record had 71 digits.

[RenYuanhua]

That is great!

[mshelikoff]

Congratulations! I took the liberty of spreading the word a little at https://www.reddit.com/r/math/commen...s_jumped_from/ .

From https://www.reddit.com/domain/mersenneforum.org/ , it looks like the forum hasn't been cited at reddit before. I hope more good than harm comes from spreading the word about this news and the forum in general.

[flagrantflowers]

Congrats!

What is the longest 'sociable sequence' -- the 79 digits cycle here being 4 terms? Is there a known limit to the number of terms a cycle can be (10, 100, 1000)?

[a1call]

Somewhat above my comprehension plane (as is with most subjects on this board), but I can recognize that Kudos are in order.

Congratulations R. Gerbicz.
All these must seem like trivial puzzles to you.

[EdH]

Great Work! R. Gerbicz!

Originally Posted by flagrantflowers

...
What is the longest 'sociable sequence' -- the 79 digits cycle here being 4 terms? Is there a known limit to the number of terms a cycle can be (10, 100, 1000)?

The longest known cycle is 28 and starts with the number 14316. It is the second one listed in David Moews' A LIST OF ALIQUOT CYCLES OF LENGTH GREATER THAN 2. There is no known limit.