Saturday, August 10

A look ahead


Now that my Leyland-prime-find farm is running and I am done with the previous-interval search that had still been running on my other Macs, I'm ready to have a look at the future of this endeavour:

 0  L(29934,157) - L(40182,47)    6243569  <66463>   24  2019 Aug 28   Aug 27
 1  L(31870,131) - L(34684,105)  11570518  <68797>   46       Oct 13   Oct 12
 2  L(34684,105) - L(29356,257)   2887602  <70425>   12       Oct 25   Oct 21
 3  L(29356,257) - L(30280,241)   6274269  <71439>   26       Nov 20   Nov 15
 4  L(30280,241) - L(104824,5)    5256668  <72700>   23       Dec 13   Dec  8
 5  L(104824,5)  - L(30247,300)   7747011  <74100>   34  2020 Jan 16
 6  L(30247,300) - L(40089,82)    8561240  <75828>   38       Feb 23
 7  L(40089,82)  - L(40746,91)   15146841  <78282>   69       May  2
 8  L(40746,91)  - L(32160,329)   5639471  <80390>   27       May 29
 9  L(32160,329) - L(40495,114)  11887307  <82129>   57       Jul 25
10  L(39070,143) - L(91382,9)    15717090  <85712>   78       Oct 11
11  L(91382,9)   - L(35829,302)   8886580  <88031>   46       Nov 26
12  L(35829,302) - L(37738,243)   6370928  <89444>   33       Dec 29
13  L(37738,243) - L(38030,249)   6038222  <90579>   32  2021 Jan 30
14  L(37614,265) - L(40210,287)  43838597  <95032>  241       Sep 28

#0 is the interval that I am currently searching. [Remember that L(x,y) = x^y+y^x, x>=y>1.] The quantity after the interval is how many Leyland numbers there are between the interval's end points. After that is a rounded-up average of the base-ten logarithms of all of those Leyland numbers — therefore, the average number of their decimal-digits size.

Following this is a ballpark estimate of how many days the interval search will require. [The 241 days (= 8 months) of the last interval suggests that it should probably be split into parts.] After this is the expected date of completion — assuming of course that all previous days-estimate are accurate, that I am able to start a new interval immediately after completing its predecessor, and that there are no hiccups, such as extended power interruptions or software/hardware failures.

When an interval is completed I will add an actual date after the estimated one so as to provide a sense of how the project is coming along.

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