Go Back > Factoring Projects > Aliquot Sequences

Thread Tools
Old 2020-12-08, 23:41   #1
Drdmitry's Avatar
Nov 2011

22×5×13 Posts
Default Small numbers with the longest 2*3 drivers

It is believed that any driver, in particular 2*3 driver, breaks sooner or later. But for how long such a driver can continue unbroken? I searched small numbers with the driver 2*3 for as long driver run as possible.

Here are the results. The smallest number with unbroken driver 2*3 for the moment is 708534. It is currently at 142 digits. Record keepers among smaller numbers are:
2010   breaks at 16 digits,  drive length 109
3306   breaks at 22 digits,  drive length 157
8154   breaks at 40 digits,  drive length 320
29070  breaks at 42 digits,  drive length 331
29190  breaks at 46 digits,  drive length 354
45570  breaks at 49 digits,  drive length 440
56562  breaks at 59 digits,  drive length 449
113454 breaks at 96 digits,  drive length 842
199290 breaks at 101 digits, drive length 821
295662 breaks at 130 digits, drive length 1371
384726 breaks at 141 digits, drive length 1348

Last fiddled with by Drdmitry on 2020-12-10 at 10:37
Drdmitry is offline   Reply With Quote
Old 2020-12-09, 02:45   #2
Romulan Interpreter
LaurV's Avatar
"name field"
Jun 2011

34·112 Posts

Very nice statistics, and most probably a lot of work behind. We did similar "studies" in the past. It should be nice if you add a column to that table, saying how many terms in the sequence the driver lasted. A good approximation is to multiply the breaking digits with a constant, assuming that the driver was there from the start. For example, D3 (2^3*3*5), with which I spent a lot of time in the past, grows like 2.8 terms per digit (iirc), while other (slower) drivers, like for example D2 (2^2*7) could grow as slow as 18 or 20 terms per digit (if no 3) or as fast as 2 to 4 terms per digit (if 3 and occasional 5).

Last fiddled with by LaurV on 2020-12-09 at 02:45
LaurV is offline   Reply With Quote
Old 2020-12-10, 10:25   #3
Drdmitry's Avatar
Nov 2011

22×5×13 Posts

I did not see a similar search here. However, to tell you the truth, I did not check too deeply.

No problem, I will add, as it does not take much time.
Drdmitry is offline   Reply With Quote

Thread Tools

Similar Threads
Thread Thread Starter Forum Replies Last Post
Use Msieve NFS for small numbers? skan Msieve 8 2013-02-26 20:35
ECM on small Mersenne Numbers Erich PrimeNet 16 2012-09-29 23:08
P-1 on small numbers Unregistered Information & Answers 2 2011-08-22 22:53
Strong Law of Small Numbers? Christenson Information & Answers 36 2011-02-16 04:29
A new Strong Law of Small Numbers example cheesehead Math 7 2009-02-06 20:49

All times are UTC. The time now is 17:28.

Wed Oct 27 17:28:49 UTC 2021 up 96 days, 11:57, 0 users, load averages: 1.31, 1.15, 1.14

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2021, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.