20160307, 21:55  #1 
"Norbert"
Jul 2014
Budapest
2·59 Posts 
y^xx^y primes
...I also search PRPs of the form y^xx^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^xx^y PRPs exists much more than y^x+x^y PRPs. For example to x= 5000 894 y^xx^y and 426 y^x+x^y PRPs, x=10000 1530 y^xx^y and 787 y^x+x^y PRPs. I have all the y^xx^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^xx^y PRPs? Last fiddled with by Batalov on 20160423 at 22:22 Reason: (only the y^xx^y part of the original message) 
20160308, 15:47  #2  
Jan 2005
Minsk, Belarus
2^{4}·5^{2} Posts 
I remember than the numbers of the form x^yy^x was factorized by Torbjörn Alm some years ago. That's his posting to ggnfs yahoogroup dated 23rd of October, 2005:
Quote:
https://groups.yahoo.com/neo/groups/ggnfs/files 

20160314, 22:51  #3 
"Norbert"
Jul 2014
Budapest
1110110_{2} Posts 
I found 2 new PRPs:
7406^12879+12879^7406, 49837 digits, 8335^12882+12882^8335, 50510 digits. Andrey, the file factortable_xyyx_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^xx^y numbers. To the y^xx^y PRPs have I nothing new found in the above group, you know y^xx^y PRPs, thats are not on my webpage? 
20160315, 19:34  #4 
Jan 2005
Minsk, Belarus
2^{4}×5^{2} Posts 
Nothing more than Henri Lifchitz's prptop + factordb.com.

20160318, 12:32  #5  
"Mark"
Apr 2003
Between here and the
6,737 Posts 
Quote:


20160318, 16:09  #6 
"Norbert"
Jul 2014
Budapest
76_{16} Posts 
Mark, I also search PRPs of the form y^xx^y.
At http://primfakt.atw.hu/ can you see, which ranges are completed and which are available for searching. 
20160326, 00:15  #7 
"Mark"
Apr 2003
Between here and the
6,737 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. 
20160402, 17:38  #8 
"Mark"
Apr 2003
Between here and the
6,737 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.

20160404, 17:03  #9 
"Mark"
Apr 2003
Between here and the
6,737 Posts 
FYI, I'm making a small change to the PRPNet server code so that server stats use y^xx^y for the  form and x^y+y^x for the + form.

20160412, 16:41  #10 
"Mark"
Apr 2003
Between here and the
6,737 Posts 
Here are a few PRPs for the minus form: It is complete to x=11400. Still crunching away.
7980^1131711317^7980 5577^1132011320^5577 3638^1132711327^3638 765^1133611336^765 3415^1134211342^3415 2181^1134411344^2181 7707^1134411344^7707 2684^1135511355^2684 2779^1136411364^2779 7287^1136611366^7287 7813^1137211372^7813 243^1138411384^243 
20160413, 22:24  #11 
"Norbert"
Jul 2014
Budapest
76_{16} Posts 
I reached x=12,970 and found 1 new PRP:
10821^12968+12968^10821, 52317 digits. Mark the y^xx^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^xx^y PRPs. 
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