20200627, 14:03  #353 
Sep 2010
Weston, Ontario
2^{3}·19 Posts 
Did you mean (for example) my original 17632 Leyland number pairs list that I reduced to 1324 candidate terms? Why not just sieve the 1324 terms?
Also, since I am not at all acquainted with xyyxsieve, is the output format of my list appropriate? I have one roundbracketed (x,y) pair per line with a final empty line to indicate endoffile. I can lose the brackets or make other changes that might make feeding xyyxsieve easier. 
20200627, 15:45  #354 
"Mark"
Apr 2003
Between here and the
2·2,927 Posts 
I can work with that file. I just need to manipulate with NotePad++ to be compatible with xyyxsieve.
Here is a sample run of xyyxsieve: Code:
xyyxsieve y100 Y2000 x1000 X1900 s+ P1e6 xyyxsieve v1.5, a program to find factors numbers of the form x^y+y^x Quick elimination of terms info (in order of check): 856401 because the term is even 162236 because x and y have a common divisor Sieve started: 3 < p < 1e6 with 694164 terms (1000 <= x <= 1900, 100 <= y <= 2000) (expecting 638964 factors) p=432389, 604.0 p/sec, 654967 factors found at 10.75K f/sec, 43.2% done. ETC 20200627 10:40 Sieve completed at p=1000193. Processor time: 93.38 sec. (0.00 sieving) (1.00 cores) 36802 terms written to xyyx.pfgw Primes tested: 78512. Factors found: 657362. Remaining terms: 36802. Time: 93.27 seconds. Code:
ABC $a^$b$c*$b^$a // Sieved to 1000193 1000 319 +1 1000 341 +1 The input has a restriction that maxy must be greater than maxy. I really don't recall why. If you have the command line tools with Xcode, you can build xyyxsieve fairly easily as a makefile is included. 
20200628, 02:31  #355 
Sep 2010
Weston, Ontario
152_{10} Posts 
If I can get it to run. After spending a considerable amount of time trying to unzip the Macversion download (it defaulted to some really old unarchivers I had squirreled away that couldn't do it), I finally downloaded a more recent app that did the job. Generally on modern Macs one can unzip a .zip file just by doubleclicking on it.
Following the Beginner's Manual, I created the shown "input.txt" file and placed it in the "distribution" folder that contained "pfgw64". Doubleclicking on pfgw64 opened Terminal and ran through the license and usage text (press enter or ^C). I think I learned that ^C actually means CtrlC. The final 'enter' (or ^C any time) always ended with a logout, after which I couldn't type my "pfgw input.txt" or anything else for that matter. 
20200628, 13:23  #356  
"Mark"
Apr 2003
Between here and the
2×2,927 Posts 
Quote:
What you need to do is open the Terminal app (Applications/Utilities). Move pfgw64 to a folder that you can access easily from the command line. It is probably under /Users/<your user id>/Downloads or /Users/<your user id>/Downloads/distribution. From there you can execute pfgw64 by typing "./pfgw64" (without the doublequotes) and hitting the enter key. I suggest typing "./pfgw64 q100^101+101^100" just to verify that it runs a PRP test on that term. Once you get that far, then you just have to replace "q100^101+101^100" with the name of a file in a pfgw compatible format. The format I showed above is compatible with pfgw. Once you get a little familiar with the Terminal app (think Unix or Linux), it opens up a world of possibilities for other command line applications such as the mtsieve suite and llr. If you have other questions, please ask. If I cannot help, there are other Mac users on this forum who can. 

20200628, 13:51  #357 
"Mark"
Apr 2003
Between here and the
13336_{8} Posts 
In trying to run xyyxsieve against your file it has issues because there each x has only one y term. With such a large range of x and y, it cannot hold everything in memory.
It would require a custom sieve to avoid excessive memory usage if one wants to do the whole range at once. I don't know if these candidates have been sieved or not or how deeply Mathematica will trial factor them to. I took a small chunk and sieved to 1e8 and reduced from 307 terms to 97 terms in about 4 minutes. It can clearly sieve more deeply. Sieving to 1e10 should reduce that to about 78 terms. If you see value in using xyyxsieve, let me know and I'll see what I can do to "whip up" a special version for your search. A "special version" would be memory friendly and twice as fast, if not faster. 
20200628, 23:48  #358 
Sep 2010
Weston, Ontario
152_{10} Posts 
Thank you so much for explaining this. I had actually used ./ on other programs before but I use Terminal so infrequently that I forgot. So I ran this on my 2013 Mac Pro which was already running PrimeQs on six separate Mathematica programs:
Code:
85085^34812+34812^85085 is composite: RES64: [13D0B9CBFDEA3D81] (3520.8900s+0.0050s) 
20200628, 23:52  #359 
Sep 2010
Weston, Ontario
2^{3}·19 Posts 
Yes, please. I do have access to 32GB RAM on most of my machines so memory may not be that critical. Thanks for doing this.

20200629, 00:17  #360  
"Mark"
Apr 2003
Between here and the
2·2,927 Posts 
Quote:
Here is the command line output from a run with that input file (running on Windows): Code:
xyyxsieve i xyyx.in P1e9 xyyxsieve v1.5, a program to find factors numbers of the form x^y+y^x Sieve started: 2 < p < 1e9 with 1324 terms (78917 <= x <= 283782, 23 <= y <= 78832) (expecting 1280 factors) p=994644191, 12.85K p/sec, 978 factors found at 70.36 sec per factor, 99.5% done. ETC 20200628 19:06 Sieve completed at p=1000000009. Processor time: 3830.22 sec. (0.03 sieving) (0.96 cores) 345 terms written to xyyx.pfgw Primes tested: 50847536. Factors found: 979. Remaining terms: 345. Time: 3984.89 seconds. I estimate that you can fully sieve and PRP test this file of terms in about 16 days. This was with AVX code (not AVX512), so only an AVX CPU will get that speed. If you don't have AVX, it will be slower. I estimate about 4x slower. I could probably double the nonAVX speed, but I assume that most people will run on a CPU that has AVX. The OpenCL code has not been updated, but it could cut the time of sieving in half, thus allowing you to sieve more deeply. 

20200629, 17:13  #361 
Sep 2010
Weston, Ontario
2^{3}×19 Posts 
Is this ready? Where do I download?

20200629, 20:21  #362 
"Mark"
Apr 2003
Between here and the
2·2,927 Posts 

20200629, 21:03  #363 
Sep 2010
Weston, Ontario
2^{3}×19 Posts 
I would like a readytorun OS X build.

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