20210311, 16:31  #452 
Sep 2010
Weston, Ontario
303_{8} 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
3^{3}·233 Posts 
Quote:


20210318, 19:39  #454 
Sep 2010
Weston, Ontario
3×5×13 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 
Sep 2010
Weston, Ontario
3·5·13 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. 
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