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-   -   Small numbers with the longest 2*3 drivers (https://www.mersenneforum.org/showthread.php?t=26292)

Drdmitry 2020-12-08 23:41

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:
[CODE]
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
[/CODE]

LaurV 2020-12-09 02:45

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).

Drdmitry 2020-12-10 10:25

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.


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