20210311, 16:31  #452 
"Hans Havermann"
Sep 2010
Weston, Ontario
2×107 Posts 
I'm guessing that I have used pfgw64 on some 5 million Leyland numbers since I started using it back in early July of last year. This is the first error encountered (this morning) using it:
Expr = 34048^5655+1*5655^34048 Detected in MAXERR>0.45 (round off check) in prp_using_gwnum Iteration: 197019/424418 ERROR: ROUND OFF 0.5>0.45 PFGW will automatically rerun the test with a1 
20210311, 18:22  #453  
"Mark"
Apr 2003
Between here and the
19·347 Posts 
Quote:


20210318, 19:39  #454 
"Hans Havermann"
Sep 2010
Weston, Ontario
2×107 Posts 
Leyland primes curve fit
I was curious about how many more new primes I was going to find in my current interval (#19) as well as the two subsequent ones (#20 & #22) so I decided to do a more formal calculation instead of my usual ballpark estimates. I first used the approach back in 2015 to calculate a best fit curve (y = Leyland number index = ax^b) for the then 954 Leyland prime indices that I believed were sequential and used that curve to decide that the prime index of L(328574,15) — still the largest known Leyland prime — would be ~5550.
I used the 2222 Leyland prime indices that I currently have as sequential to recalculate the best fit. In the attached, that curve is red, contrasted with a green curve for the 2015 calculation. The green curve actually holds up pretty well until we get to ~1800. The recalculated L(328574,15) now comes in at index ~5908. But I wanted to know how many new primes I was going to find in the next couple of months. For interval #19, the suggested total will be ~88 (I have 80 as I write with another week or so to go). Interval #20 will yield ~90 and #22, ~97. 
20210327, 14:38  #455 
"Hans Havermann"
Sep 2010
Weston, Ontario
214_{10} Posts 
I have examined all Leyland numbers in the seven gaps between L(48694,317) <121787>, #2221, and L(44541,746) <127955> and found 111 new primes. That makes L(44541,746) #2339.
So much for my March 18th calculated prediction (for this interval) of only 88 new primes. I do update a sortablecolumns version of my Leyland primes indexing page when I finish an interval or find a prime with a y smaller than 1000. But it's too much effort to update it every time I find a new prime as I have to make three corrections to the html after each page conversion. 
20210430, 00:51  #456 
"Hans Havermann"
Sep 2010
Weston, Ontario
2×107 Posts 

20210601, 15:50  #457 
"Hans Havermann"
Sep 2010
Weston, Ontario
326_{8} Posts 
As my search of interval #22 winds down (ten or so day to go), I started (yesterday) the interval from L(299999,10) to L(300999,10). A preliminary estimate suggests that this will require some twoandahalf months.

20210608, 18:31  #458 
"Norbert"
Jul 2014
Budapest
3·37 Posts 
Another new PRP:
45^104608+104608^45, 172940 digits. 
20210609, 10:28  #459  
"Hans Havermann"
Sep 2010
Weston, Ontario
2·107 Posts 
Quote:
I believe that we have now all Leyland primes/PRPs < 150000 decimal digits or, equivalently, all prime/PRP L(x,y), x < 33180. 

20210610, 09:06  #460 
Aug 2020
79*6581e4;3*2539e3
503 Posts 
Impressive compilation. Do you have data on which of the numbers are just PRPs? It would make a nice list of candidates for primo.

20210610, 10:09  #461 
Mar 2006
Germany
5610_{8} Posts 
You can look at this table for a list of unproven numbers. I've not looked at those for a longer time, so some are verified and a certificate is available at FactorDB.
Just updated only 3 numbers, see the recent changes. Dates and program taken from FDB. Last fiddled with by kar_bon on 20210610 at 10:09 
20210610, 14:31  #462 
Aug 2020
79*6581e4;3*2539e3
503 Posts 
Ok, thanks.

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