mersenneforum.org  

Go Back   mersenneforum.org > Factoring Projects > XYYXF Project

Reply
 
Thread Tools
Old 2021-03-11, 16:31   #452
pxp
 
pxp's Avatar
 
Sep 2010
Weston, Ontario

3108 Posts
Default

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
pxp is offline   Reply With Quote
Old 2021-03-11, 18:22   #453
rogue
 
rogue's Avatar
 
"Mark"
Apr 2003
Between here and the

2×32×353 Posts
Default

Quote:
Originally Posted by pxp View Post
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
That does happen, but is rare. Fortunately it tried with a different FFT size automatically.
rogue is offline   Reply With Quote
Old 2021-03-18, 19:39   #454
pxp
 
pxp's Avatar
 
Sep 2010
Weston, Ontario

23·52 Posts
Default 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.
Attached Thumbnails
Click image for larger version

Name:	LeylandPrimesCurveFit.png
Views:	99
Size:	79.1 KB
ID:	24535  
pxp is offline   Reply With Quote
Old 2021-03-27, 14:38   #455
pxp
 
pxp's Avatar
 
Sep 2010
Weston, Ontario

110010002 Posts
Default

Quote:
Originally Posted by pxp View Post
That makes L(48694,317) #2221.
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 sortable-columns 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.
pxp is offline   Reply With Quote
Old 2021-04-30, 00:51   #456
pxp
 
pxp's Avatar
 
Sep 2010
Weston, Ontario

23×52 Posts
Default

Quote:
Originally Posted by pxp View Post
That makes L(44541,746) #2339.
I have examined all Leyland numbers in the four gaps between L(44541,746) <127955>, #2339, and L(49205,532) <134129> and found 99 new primes. That makes L(49205,532) #2442 and advances the index to L(49413,580), #2485.
pxp is offline   Reply With Quote
Old 2021-06-01, 15:50   #457
pxp
 
pxp's Avatar
 
Sep 2010
Weston, Ontario

110010002 Posts
Default

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 two-and-a-half months.
pxp is offline   Reply With Quote
Old 2021-06-08, 18:31   #458
NorbSchneider
 
NorbSchneider's Avatar
 
"Norbert"
Jul 2014
Budapest

109 Posts
Default

Another new PRP:
45^104608+104608^45, 172940 digits.
NorbSchneider is offline   Reply With Quote
Old 2021-06-09, 10:28   #459
pxp
 
pxp's Avatar
 
Sep 2010
Weston, Ontario

23×52 Posts
Default

Quote:
Originally Posted by pxp View Post
That makes L(49205,532) #2442 and advances the index to L(49413,580), #2485.
I have examined all Leyland numbers in the two gaps between L(49413,580) <136550>, #2485, and L(49878,755) <143547> and found 123 new primes. That makes L(49878,755) #2610 and advances the index to L(45728,1905), #2691.

I believe that we have now all Leyland primes/PRPs < 150000 decimal digits or, equivalently, all prime/PRP L(x,y), x < 33180.
pxp is offline   Reply With Quote
Old 2021-06-10, 09:06   #460
bur
 
bur's Avatar
 
Aug 2020

4548 Posts
Default

Impressive compilation. Do you have data on which of the numbers are just PRPs? It would make a nice list of candidates for primo.
bur is offline   Reply With Quote
Old 2021-06-10, 10:09   #461
kar_bon
 
kar_bon's Avatar
 
Mar 2006
Germany

1011010111002 Posts
Default

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 2021-06-10 at 10:09
kar_bon is offline   Reply With Quote
Old 2021-06-10, 14:31   #462
bur
 
bur's Avatar
 
Aug 2020

12C16 Posts
Default

Ok, thanks.
bur is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
Leyland Primes: ECPP proofs Batalov XYYXF Project 19 2021-07-20 21:07
Mersenne Primes p which are in a set of twin primes is finite? carpetpool Miscellaneous Math 3 2017-08-10 13:47
Distribution of Mersenne primes before and after couples of primes found emily Math 34 2017-07-16 18:44
On Leyland Primes davar55 Puzzles 9 2016-03-15 20:55
possible primes (real primes & poss.prime products) troels munkner Miscellaneous Math 4 2006-06-02 08:35

All times are UTC. The time now is 06:03.


Mon Aug 2 06:03:25 UTC 2021 up 10 days, 32 mins, 0 users, load averages: 1.21, 1.22, 1.23

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2021, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.