20190611, 06:26  #254 
Sep 2010
Weston, Ontario
A6_{16} Posts 
I have examined all Leyland numbers in the gap between L(28468,129) <60085>, #1226, and L(19021,1576) <60821> and found 9 new primes. That makes L(19021,1576) #1236 and advances the index to L(19898,1263), #1254.

20190707, 02:01  #255  
Sep 2010
Weston, Ontario
2·83 Posts 
Quote:
I count 160 unindexed primes in my list. I'm going to be adding some more cores to the project next month, so I'm looking forward to seeing what the number will be in six months. My Leyland prime indexing effort is of course just a file on my computer. I'm getting old and there will come a time when that domain no longer reaches that document and any thenexisting versions out there may not reflect its latest changes. For that reason, I am now keeping a backup copy on my Google Drive that will hopefully be accessible a little longer than the file on my computer. Just in case anyone is interested. 

20190707, 02:37  #256  
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
2·3·1,709 Posts 
Quote:
May I suggest that you add an indication whether primality is known to have been proven or whether the number has sofar only passed a PRP test? 

20190707, 12:32  #257  
Sep 2010
Weston, Ontario
2·83 Posts 
Quote:
It might be enough to collate the "proven" primes in Andrey Kulsha's list augmented by RichD's 27 subsequent additions and I might do that. But that takes us only to November 2017 and constitutes a blog post at most. 

20190707, 13:43  #258  
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
2×3×1,709 Posts 
Quote:


20190708, 05:00  #259 
Sep 2010
Weston, Ontario
2×83 Posts 
I've created a Proven Leyland Primes document of the Leyland primes up to L(8656,2929), #715. In the final column I've indicated factordb if factordb.com has the number as P. I've indicated Kulsha if factordb.com has the number as PRP but Andrey Kulsha's list suggests it is proven. I count 257 of the former (which excludes index #1) and 31 of the latter, for a total of 288 proven primes.
I believe Kulsha's list has 260 entries for proven primes and RichD had 27 additions for a total of 287. The missing prime appears to be L(3028,483). 
20190708, 07:10  #260  
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
2·3·1,709 Posts 
Quote:
Paul 

20190715, 09:23  #261 
Sep 2010
Weston, Ontario
2×83 Posts 

20190720, 09:19  #262 
Mar 2006
Germany
2·1,423 Posts 
I've created a category for Leyland primes/PRPs in the Wiki here.
The templates takes the number of digits for sorting so not for ascending xvalues. The table of all numbers is sortable by any column inserted a counting column so you can sort by date found or proven. @pxp: I'm using the full date of findings from FactorDB, is this correct here? (see last examples) You gave only year/month in your list. Is there a rule to determine the Leyland # I could use instead of giving as parameter of any number? The same can be done for x^y  y^x then. 
20190720, 14:39  #263  
Sep 2010
Weston, Ontario
2·83 Posts 
Quote:
The Leyland # of a given L(x,y) is given by its position in OEIS sequence A076980. The easiest way to associate a given L(x,y) with its Leyland # is to simply sort all Leyland numbers up to a specified decimaldigit size. I did this back in 2015 for Leyland numbers up to ~100000 decimaldigit size: >331 million (x,y) pairs. The difficulty is in the storing/sorting of large Leyland numbers that are approximately equal, for example: (240240,2), (120120,4), (80080,8), (60060,16), (48048,32), (40040,64), (34320,128), (30030,256), (24024,1024), (21840,2048), (20020,4096), (18480,8192), and (17160,16384). I subsequently developed a Mathematica procedure for determining the Leyland # of any given (x,y) that does a count based on L(x,y) approximations up to a digitsize slightly smaller than the digitsize of L(x,y) and then adding a count for exact L(x,y) in the final stretch. Still, it took me 13 hours to determine the Leyland # of Serge Batalov's L(328574,15). Indices for x^y  y^x numbers would (ideally) correspond to their position in A045575. For numbers larger than ~10^218 (the limit of how many terms are listed in the bfile for that sequence) I suppose that's as easy/hard as the corresponding x^y + y^x situation. 

20190720, 18:55  #264  
Sep 2010
Weston, Ontario
2·83 Posts 
Quote:
For example, Anatoly Selevich's L(8656,2929) has a FactorDB createtime of "before November 4, 2018" which is a far cry from his discovery date of ~ November 2007. When I went through the first 715 primes in FactorDB last week for my provenprimes list, I noted that for fifteen or twenty (or so) my query was the first query for that number (appearing as U). I just now tried it with 7789^7302+7302^7789 (prime #716) and it came back as U. So there are plenty of unknown/untried primes still that are not yet in FactorDB. The FactorDB creation date therefore strikes me as unindicative of the the prime's discovery date, except (as noted) for people like myself. 

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