y^x-x^y primes

NorbSchneider · 2016-03-07, 21:55

...I also search PRPs of the form y^x-x^y.

I made a webpage to these PRPs, similar to Andrey's page
to the y^x+x^y PRPs. You can find the page at primfakt.atw.hu,
y^x-x^y PRPs exists much more than y^x+x^y PRPs.
For example to x= 5000 894 y^x-x^y and 426 y^x+x^y PRPs,
x=10000 1530 y^x-x^y and 787 y^x+x^y PRPs.
I have all the y^x-x^y PRPs to x=10800, and a few for higher x values.
Andrey, Hans or someone else, are you interesting to join me
searching the y^x-x^y PRPs?

XYYXF · 2016-03-08, 15:47

I remember than the numbers of the form x^y-y^x was factorized by Torbjörn Alm some years ago. That's his posting to ggnfs yahoogroup dated 23rd of October, 2005:

Quote:

I have been running a little factoring job on numbers
X^Y-Y^X and I have factored almost all numbers up to X=80.
I wonder if there is any interest in the result and where to
publish it.

The factoring has been done spep by step with
trial div up to 10^7, P-1, P+1 and rho followed by MPQS and ECM
in order to remove small factors. Some numbers has been factored
algebraic at this point.
Finally SNFS + some GNFS to break the composites. I have a database in
Paradox to keep it and a Delphi prgoram to administer it.
I have kept all GNFS/SNFS result files as well as the log files.

If there is an interest , I will gladly made it available as
a text file or as a PDF document.

Torbjörn Alm

Some of the results is still available in the Files section of the group:
https://groups.yahoo.com/neo/groups/ggnfs/files

NorbSchneider · 2016-03-14, 22:51

I found 2 new PRPs:
7406^12879+12879^7406, 49837 digits,
8335^12882+12882^8335, 50510 digits.

Andrey, the file factortable_xy-yx_1_100.txt in https://groups.yahoo.com/
neo/groups/ggnfs/files group contains all factorization for x < 101 as
in your results.txt. For 100 < x < 151 as in your results2.txt have I
nothing found to the y^x-x^y numbers.

To the y^x-x^y PRPs have I nothing new found in the above group,
you know y^x-x^y PRPs, thats are not on my webpage?

XYYXF · 2016-03-15, 19:34

Nothing more than Henri Lifchitz's prptop + factordb.com.

rogue · 2016-03-18, 12:32

Quote:

Originally Posted by pxp

New PRP: L(15215,4762). I'm still working on eight gaps but that's down from as many as eighteen, having diverted processes to another project: smallest prime containing a given number of zeros. So I don't see myself doing y^x-x^y, Norbert. If anything, after I've had my fill of this diversion, I'll get back to advancing my indexing full on.

y^x-x^y sounds like an interesting project. I have a couple of week left for the project I am currently working on. I could probably start working on that soon after.

NorbSchneider · 2016-03-18, 16:09

Mark, I also search PRPs of the form y^x-x^y.
At http://primfakt.atw.hu/ can you see, which ranges are completed and which
are available for searching.

rogue · 2016-03-26, 00:15

I started sieving for x=11301 to x=12400. Unfortunately I only have one computer that I can run my sieving code on and that is the one with the slowest GPU. Now if I could only talk my wife into letting me get a new 27" iMac...

Down to 650,000 (from nearly 3,000,000) and only sieved to 131,519.

rogue · 2016-04-02, 17:38

Sieving is done. I have about 400,000 candidates to test. I'm guessing about 40 days of PRP testing, but only after I suspect what I am currently doing.

rogue · 2016-04-04, 17:03

FYI, I'm making a small change to the PRPNet server code so that server stats use y^x-x^y for the - form and x^y+y^x for the + form.

rogue · 2016-04-12, 16:41

Here are a few PRPs for the minus form: It is complete to x=11400. Still crunching away.

7980^11317-11317^7980
5577^11320-11320^5577
3638^11327-11327^3638
765^11336-11336^765
3415^11342-11342^3415
2181^11344-11344^2181
7707^11344-11344^7707
2684^11355-11355^2684
2779^11364-11364^2779
7287^11366-11366^7287
7813^11372-11372^7813
243^11384-11384^243

NorbSchneider · 2016-04-13, 22:24

I reached x=12,970 and found 1 new PRP:
10821^12968+12968^10821, 52317 digits.

Mark the y^x-x^y PRPs page is updated, the new PRPs from you and me
are on the page now.

Hans, the Leyland# to a given (x,y) pair determine you also with a database
and a Mathematica program, thank for sharing this. I try to write a program
in C# to determine the "Leyland#" to the y^x-x^y PRPs.

2016-03-07, 21:55	#1
NorbSchneider "Norbert" Jul 2014 Budapest 109 Posts	y^x-x^y primes ...I also search PRPs of the form y^x-x^y. I made a webpage to these PRPs, similar to Andrey's page to the y^x+x^y PRPs. You can find the page at primfakt.atw.hu, y^x-x^y PRPs exists much more than y^x+x^y PRPs. For example to x= 5000 894 y^x-x^y and 426 y^x+x^y PRPs, x=10000 1530 y^x-x^y and 787 y^x+x^y PRPs. I have all the y^x-x^y PRPs to x=10800, and a few for higher x values. Andrey, Hans or someone else, are you interesting to join me searching the y^x-x^y PRPs? Last fiddled with by Batalov on 2016-04-23 at 22:22 Reason: (only the y^x-x^y part of the original message)

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2016-03-14, 22:51	#3
NorbSchneider "Norbert" Jul 2014 Budapest 109 Posts	I found 2 new PRPs: 7406^12879+12879^7406, 49837 digits, 8335^12882+12882^8335, 50510 digits. Andrey, the file factortable_xy-yx_1_100.txt in https://groups.yahoo.com/ neo/groups/ggnfs/files group contains all factorization for x < 101 as in your results.txt. For 100 < x < 151 as in your results2.txt have I nothing found to the y^x-x^y numbers. To the y^x-x^y PRPs have I nothing new found in the above group, you know y^x-x^y PRPs, thats are not on my webpage?

2016-03-15, 19:34	#4
XYYXF Jan 2005 Minsk, Belarus 400₁₀ Posts	Nothing more than Henri Lifchitz's prptop + factordb.com.

2016-03-18, 16:09	#6
NorbSchneider "Norbert" Jul 2014 Budapest 109 Posts	Mark, I also search PRPs of the form y^x-x^y. At http://primfakt.atw.hu/ can you see, which ranges are completed and which are available for searching.

2016-03-26, 00:15	#7
rogue "Mark" Apr 2003 Between here and the 11×577 Posts	I started sieving for x=11301 to x=12400. Unfortunately I only have one computer that I can run my sieving code on and that is the one with the slowest GPU. Now if I could only talk my wife into letting me get a new 27" iMac... Down to 650,000 (from nearly 3,000,000) and only sieved to 131,519.

2016-04-02, 17:38	#8
rogue "Mark" Apr 2003 Between here and the 18CB₁₆ Posts	Sieving is done. I have about 400,000 candidates to test. I'm guessing about 40 days of PRP testing, but only after I suspect what I am currently doing.

2016-04-04, 17:03	#9
rogue "Mark" Apr 2003 Between here and the 11·577 Posts	FYI, I'm making a small change to the PRPNet server code so that server stats use y^x-x^y for the - form and x^y+y^x for the + form.

2016-04-12, 16:41	#10
rogue "Mark" Apr 2003 Between here and the 14313₈ Posts	Here are a few PRPs for the minus form: It is complete to x=11400. Still crunching away. 7980^11317-11317^7980 5577^11320-11320^5577 3638^11327-11327^3638 765^11336-11336^765 3415^11342-11342^3415 2181^11344-11344^2181 7707^11344-11344^7707 2684^11355-11355^2684 2779^11364-11364^2779 7287^11366-11366^7287 7813^11372-11372^7813 243^11384-11384^243

2016-04-13, 22:24	#11
NorbSchneider "Norbert" Jul 2014 Budapest 155₈ Posts	I reached x=12,970 and found 1 new PRP: 10821^12968+12968^10821, 52317 digits. Mark the y^x-x^y PRPs page is updated, the new PRPs from you and me are on the page now. Hans, the Leyland# to a given (x,y) pair determine you also with a database and a Mathematica program, thank for sharing this. I try to write a program in C# to determine the "Leyland#" to the y^x-x^y PRPs.