20190728, 11:20  #276 
Mar 2006
Germany
2×1,423 Posts 
I've made some changes/approvements in the Wiki for Leyland primes/PRPs:
The latest PRP can be found here  added a history entry to give the post# with date  the "date found" from FactorDB  not yet Leyland# filled There's also a "Proved" history entry possible: see here  "Prove date" and "Program" from FactorDB  History date from forum post with link There're also different categories for proven primes and PRP. Because of sorting by digits, the smallest unproven number can be found as first entry here = Leyland prime P 3147 214 = 7334 digits. This can help to identify and prove smaller PRPs for others. In the table view the numbers which marked "proven" but no proof is available in FactorDB are marked. Further there's a page which creates a CSV format to copy/paste for further use. I'm now going to insert more/all known Leyland numbers in the wiki with data I've found:  proven dates/names from the other thread (most from RichD) and found dates from here  dates from old primes from Leyland page as "When reserved"/"When completed". 
20190730, 16:43  #277 
Mar 2006
Germany
5436_{8} Posts 
I don't know if this was shown somewhere but found nothing, so here's the current distribution of known Leyland primes/PRP's for x<40000 and y<25000:

20190731, 11:05  #278 
Sep 2010
Weston, Ontario
167 Posts 
I recognize those 100000digit numbers on the right. :) I played in Mathematica with a similar graph last night with the idea of superimposing curves of 60000, 80000, and 100000digit x^y+y^x but I couldn't even figure out how to generate those curves. :/

20190731, 17:53  #279 
Sep 2010
Weston, Ontario
167 Posts 
I finally kludged something together (ContourPlot was the Mathematica function that I was missing). I'm not sure if the waves on the end of the <60000> curve are real or an artifact.

20190731, 18:06  #280  
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
24020_{8} Posts 
Quote:
Above about, say, 8000,the distribution of the points looks to me very much like a uniformly random sample of the triangle. Presumably it is not, or the distribution would look random at the lower regions as well. It may be interesting to apply a scaling to the Y values, such that the populated area becomes square and then to investigate the hypothesis that the (x,y) coordinates are drawn independently from a uniform random distribution. If the likelihood is significantly different try to discover a distribution which better matches the observations. Any takers? I'm not sure my statistics ability is (yet) up to the task. (added in edit: Henry,this seems like an area where you have some expertise.) Last fiddled with by xilman on 20190731 at 18:11 

20190731, 23:44  #281 
Sep 2010
Weston, Ontario
167 Posts 
Indeed. I've fixed that, fixed the aspect ratio to make the x=y line bisect the axes, made the points smaller, and added two greenish curves to indicate the interval that I am currently exploring (I should be done in ten days).

20190810, 11:57  #282 
Sep 2010
Weston, Ontario
167 Posts 

20190810, 16:03  #283 
Sep 2010
Weston, Ontario
167 Posts 
A look ahead
I have written a blog article regarding my ambitious Leylandprime search schedule for the next two years.

20190823, 17:10  #284 
"Norbert"
Jul 2014
Budapest
5·19 Posts 
Another new PRP:
7257^17528+17528^7257, 67672 digits. 
20190827, 22:18  #285 
Sep 2010
Weston, Ontario
167 Posts 

20190918, 08:52  #286 
"Norbert"
Jul 2014
Budapest
5·19 Posts 
Another new PRP:
12511^17556+17556^12511, 71933 digits. 
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