Leyland Primes (x^y+y^x primes)

[pxp]

Originally Posted by rogue

The ABC line needs to have "// Sieved to xxx" on the first line when used as input. This is probably the issue you are seeing. Nevertheless I can see if anything else is wrong.

Adding the comment made no difference.

I noticed that the help file had sieve start "3" as the default, suggesting perhaps that -p2 might be an out of range argument. As a result, I reworked my shared pages to exclude even L(x,y). That brings the number of terms per page down from ~11000 to ~7300. The first three lines of my first page are now:

ABC $a^$b$c*$b^$a // Sieved to 3
102503 5888 +1
80340 64561 +1

[chris2be8]

rogue, can you post a sample file that works for you. Then pxp can run that to check his binary is OK, then change 1 thing at a time until it's doing what he wants. I've found that starting from a working example makes problem solving much easier.

Chris

[rogue]

Apparently I did not do a "make clean" before I did the make. The attached should work with the proper ABC file.

I also found an issue in avx_powmod that only impacts non-Windows builds. That is also fixed.

./xyyxsieve -ixyyx.in -p3 -P1e6
xyyxsieve v1.5, a program to find factors numbers of the form x^y+y^x
Sieve started: 3 < p < 1e6 with 1324 terms (78917 <= x <= 283782, 23 <= y <= 78832) (expecting 1219 factors)
Sieve completed at p=1000193.
Processor time: 13.87 sec. (0.00 sieving) (0.98 cores)
503 terms written to xyyx.pfgw
Primes tested: 78512.  Factors found: 821.  Remaining terms: 503.  Time: 14.16 seconds.

[pxp]

Originally Posted by rogue

The attached should work with the proper ABC file.

mm5:~ pxp$ cd /Users/pxp/Desktop/rogue 
mm5:rogue pxp$ ./xyyxsieve -i386434.txt -p3 -P2e9
xyyxsieve v1.5, a program to find factors numbers of the form x^y+y^x
Sieve started: 3 < p < 2e9 with 7203 terms (78911 <= x <= 1283705, 2 <= y <= 78900) (expecting 6834 factors)
  
p=5957291, 4.586K p/sec, 6757 factors found at 1.52 sec per factor, 0.3% done. ETC 2020-07-03 06:54          
p=10411189, 4.588K p/sec, 6768 factors found at 5.53 sec per factor, 0.5% done. ETC 2020-07-03 02:52         
p=14994013, 4.595K p/sec, 6775 factors found at 8.68 sec per factor, 0.7% done. ETC 2020-07-03 01:09         
p=24406297, 4.597K p/sec, 6785 factors found at 12.15 sec per factor, 1.2% done. ETC 2020-07-02 23:34        
p=29201503, 4.594K p/sec, 6789 factors found at 15.19 sec per factor, 1.5% done. ETC 2020-07-02 23:08        
p=34041223, 4.597K p/sec, 6794 factors found at 12.15 sec per factor, 1.7% done. ETC 2020-07-02 22:48        
p=38899507, 4.573K p/sec, 6798 factors found at 15.18 sec per factor, 1.9% done. ETC 2020-07-02 22:33        
p=43805231, 4.583K p/sec, 6800 factors found at 30.36 sec per factor, 2.2% done. ETC 2020-07-02 22:21

This is on one of my Mac minis. I'll let it run to the end. Thank you!

[rogue]

Originally Posted by pxp

This is on one of my Mac minis. I'll let it run to the end. Thank you!

You're welcome. Glad to be of service.

You can use ^C to stop at any time. The program will finish processing the current chunk, then save and exit.

If 2e9 isn't deep enough you can start sieving again using -ixyyx.pfgw. You will not need to use -p as it will grab the initial prime from the input file.

[pxp]

Processor time: 22549.57 sec. (1.62 sieving) (0.99 cores)
333 terms written to xyyx.pfgw
Primes tested: 98222288.  Factors found: 6870.  Remaining terms: 333.  Time: 22668.14 seconds.

I took this up to 5e9 which required an additional 8.5 hours and found 16 new factors, slightly less than 2 new factors per hour. On my Mac mini, a PRP-test of a number this size required half an hour, so roughly equivalent to what subsequent sieving might accomplish. I have replaced my three previously shared pre-sieved Leyland number files with their post-sieved outputs:

http://chesswanks.com/num/LLPHbdl/386434.txt
http://chesswanks.com/num/LLPHbdl/386435.txt
http://chesswanks.com/num/LLPHbdl/386436.txt

They contain 317, 325, and 303 terms, respectively. I think I can PRP-test any one of these in under a week and I intend to try in the near future. But first I will generate more sieved pages.

I ran multiple terminal windows to generate the three files. My initial attempt at this ran off the same xyyxsieve, little realizing that the ongoing xyyx.pfgw files overwrote each other. So I ended up cloning the folder containing xyyxsieve and re-ran each terminal window off its own folder. I suppose a future version of xyyxsieve could output a .pfgw file with a name that matches the input file name.

[rogue]

Originally Posted by pxp

I ran multiple terminal windows to generate the three files. My initial attempt at this ran off the same xyyxsieve, little realizing that the ongoing xyyx.pfgw files overwrote each other. So I ended up cloning the folder containing xyyxsieve and re-ran each terminal window off its own folder. I suppose a future version of xyyxsieve could output a .pfgw file with a name that matches the input file name.

You can have multiple tabs in a Terminal window or multiple Terminal windows.

You can override the name of the output file by using -o and specifying the file name.

[LaurV]

Originally Posted by kar_bon

So your file is like

(85085,34812)
(92856,14509)

Do this with a text editor:
- remove the "("
- remove the ")"
- replace the "," with " +1 " (notice the spaces)

Now the file should look like this

85085 +1 34812
92856 +1 14509

I didn't keep the track of the development you talk about here, but what is described by Karsten can be achieved with a single regex command using perl or any text editor that accepts regex search and replace. For example, to do this with pn2 or with notepad++, open a search/replace box, by pressing ctrl+f or ctrl+h or alt+r (depending on the program or OS or settings you have for shortcuts) or just take it from the menu, then go to replace tab, be careful to check the "regular expressions" box, then in the "find what" box type "^\((\d*),(\d*)\)$" (without quotes, grrrr! how do I tell the forum's matjax not to mess with my expression? what a crakpot haha, he thinks this is math ...Should I use "code" tags?) and in the "replace with" box type "\1 +1 \2" (without quotes, and mind the spaces around the "+1"). Click "replace all.

To have the plus at the end, just use "\1 \2 +1" in the "replace with" box.

For who didn't hear about regular expressions, this translates to "if you find two groups of any number of digits each, alone on the row (i.e. no other text, the ^ and $ signs represent beginning and end of the row) which are between parenthesis and separated by c comma, extract the the two groups in two different strings (called \1 and \2, this is what the internal parenthesis do, in the "find what" string) and rearrange them according with the "replace with" box, possibly adding some text (the +1 and spaces) around them". That's all. No magic.

Or, actually, Magic!
You still need to add the header line "ABC blah blah" by hand (i.e. typing )
Edit: picture (Notepad++ used for exemplification) because Mathjax messed my expression, I know there was a way to block this, which Serge wrote here in the past, but we forgot the tag... was it "noeval", or what?



One more observation, in Notepad++ the regex search/replace is undo-able (if you mess the expression, just press undo and retry till you learn the right way)

[pxp]

Originally Posted by pxp

http://chesswanks.com/num/LLPHbdl/386434.txt
http://chesswanks.com/num/LLPHbdl/386435.txt
http://chesswanks.com/num/LLPHbdl/386436.txt

They contain 317, 325, and 303 terms, respectively. I think I can PRP-test any one of these in under a week and I intend to try in the near future. But first I will generate more sieved pages.

There are now 45 sieved pages available for Leyland prime candidates larger than L(328574,15), running from 386434 to 386478 decimal digits. Just replace the number in the URL with the number of decimal digits you want. I have started a pfgw test on the last six of those pages (386473-386478) and I realize now that my previous estimate of 30 minutes per term was incorrect. It is closer to 48 minutes. The difference, I believe, is likely due to the fact that running six pfgw tests concurrently throttles the single-pfgw-test processor speed back to its base value. So this will take 10-11 days for me total.

I don't of course expect to find a PRP. It strikes me as unlikely that any of the 45 pages will yield one. But don't let that put you off willing to look. Every eliminated page brings us closer to that eventual new largest-known Leyland prime.

[henryzz]

Am I correct in thinking you are sieving each digit length separately? Is there any advantage in doing this? How does combining digit lengths affect sieve speed?

[pxp]

Originally Posted by henryzz

Am I correct in thinking you are sieving each digit length separately? Is there any advantage in doing this? How does combining digit lengths affect sieve speed?

Sorting Leyland numbers by digit-length — more properly, by absolute magnitude — has been my obsession from the get-go. Mark hacked the existing program to accommodate any Leyland-number input file, including my sorted ones.