Leyland Primes (x^y+y^x primes) - Page 25

kar_bon · 2019-07-20, 20:12

Yes, the "date" "before November 4, 2018" in FactorDB was created after server/database moving by Markus, so not available older dates here.

The list of Leyeland primes contains also some dates like for x=1031-1050 as reserved/complete, that's why I used "2001-06-04" for those 4 primes then. For other dates expressions like "2002-06" is enough here as you gave for >#294 in your list.

Dates from your and Norberts finds should be better than.

Will see how this can be handled. The great advantage of the table is the individual sorting:
I tried first to sort by x-value in the category by the template, but this needed a click to sort the table by digits. Now it's done by sorting by digits and calling the table only. Inserting a new number you don't need to create an index (first column), it's done in the table call.
Also:
Clicking on "Digits" column first (upwards sorting) and than on "Prover" the smallest unproven number are listed in descending digit order: could be helpful to prove some smaller numbers.

ToDo's:
pages with information about those numbers, links, stats, current work/reservation, minus-side.

kar_bon · 2019-07-22, 13:59

Here is a Leyland prime of 4345 digits without a certificate in FactorDB but proven prime in the list.

Same here: 4826 digits.

pxp · 2019-07-22, 16:08

Quote:

Originally Posted by kar_bon

Here is a Leyland prime of 4345 digits without a certificate in FactorDB but proven prime in the list.
Same here: 4826 digits.

Yes. These are the smallest two of thirty-one instances previously noted here. You can easily find all 31 by searching for the word 'Kulsha' in my proven Leyland primes list.

NorbSchneider · 2019-07-23, 11:42

I found 3 new PRPs:
634^42803+42803^634, 119938 digits,
736^44335+44335^736, 127104 digits,
9946^17491+17491^9946, 69923 digits.

kar_bon · 2019-07-24, 11:14

Those three new ones are in the Wiki, too.

Some notes:

- I'm using a date of discovery for old Leyland primes according to the "When completed" listed here. So listing/sorting in the table is available for those, too.

- Primes with missing certificate in FactorDB are marked with a remark in the page and listed as orange in column "Prover" in the table. These certs should be inserted later.

- I've found some certs. in FactorDB but not yet listed in pxp's list. I used the date and info of program from FactorDB.

- I've inserted some discovery dates for numbers found during doublechecking from here.

- Categories for proven and PRPs numbers available now.

More to come.

pxp · 2019-07-24, 17:12

Quote:

Originally Posted by kar_bon

I've found some certs. in FactorDB but not yet listed in pxp's list.

I'm not sure what you are saying here. There were only two types of proven Leyland primes in my list: Those that were shown as P in FactorDB (257, indicated by the word 'factordb') and those that were shown as PRP in FactorDB but were indicated as proven by Kulsha (31, indicated by the word 'Kulsha'). If you are saying that there are certificates in the former, that's certainly to be expected. I wasn't concerned about certificates in creating my list but only in distinguishing proven primes from PRPs.

Dylan14 · 2019-07-24, 17:30

Reserving the range x = 20001-30000, y = 801-1000.

kar_bon · 2019-07-24, 18:37

Quote:

Originally Posted by pxp

I'm not sure what you are saying here.

I'm trying to combine several data files but found no prover/date in any.

Example: L(2448,535) no dates for <#295 in you a094133.txt and no prover/proven date at all, so I used the data from FactorDB.

pxp · 2019-07-24, 22:00

Quote:

Originally Posted by kar_bon

I'm trying to combine several data files but found no prover/date in any. Example: L(2448,535) no dates for <#295 in you a094133.txt and no prover/proven date at all, so I used the data from FactorDB.

The point of my a094133.txt document is to have in one place an up-to-date list of all known Leyland primes and to track my continuing effort to index them by size. I've added the Leyland#, decimal-digit size, discoverer, and the discovery date for indices >294 (PRPtop did not accept PRPs smaller than 10000 decimal digits and I've culled my discovery dates primarily from them, except where they were missing or clearly incorrect).

I was never very interested in the proven/PRP distinction and created the proven Leyland primes list only as a courtesy to xilman who asked me for something like it on July 6. Andrey Kulsha's list has prover/proven-date information on 260 of the known proven Leyland primes, including 31 that are still PRP in FactorDB. For these 31 you will not be able to get prover/proven-date from FactorDB. For the remaining 229 you can get the information from either Kulsha's list or from FactorDB but I would guess that the FactorDB prover/proven-date may or may not agree with Kulsha's. To grab a random example: L(3100,11) is proven prime by Jonathan A. Zylstra on 30 December 2003 according to Kulsha. It is proven prime by Edwin Hall on 15 March 2017 according to FactorDB. Clearly Kulsha's information is likely to be preferred.

There are 28 proven Leyland primes that are not in Kulsha's list and for these one necessarily has to rely on FactorDB alone. But these are easy. 27 of them are from RichD (the last three posts here) and one is from Anonymous.

pxp · 2019-07-24, 22:47

Quote:

Originally Posted by Dylan14

Reserving the range x = 20001-30000, y = 801-1000.

Hey Dylan. Welcome aboard.

Just so you know, Andrey Kulsha has been missing (I'm guessing that he died) since his last update in January 2017, so there is really no-one here to track the reservations. Since January 2017 there have only been two users that are actively searching for new Leyland primes: Norbert Schneider who has added 33 and myself who has added 177. Those 210 combined with the 1250 in Kulsha's list give us the 1460 known Leyland primes to date.

While Norbert still conducts his searches by using the (x,y)-range system, I do not. My searches are strictly by L(x,y) decimal-digit size and my current search interval is L(32907,92) <64623 decimal digits> to L(29934,157) <65733>.

Be sure to post any of your finds to either PRPtop or here (preferably both) so that I can add them to my own list of known Leyland primes.

NorbSchneider · 2019-07-27, 16:58

Another new PRP:
746^44541+44541^746, 127955 digits.

2019-07-22, 13:59	#266
kar_bon Mar 2006 Germany 2²·727 Posts	Here is a Leyland prime of 4345 digits without a certificate in FactorDB but proven prime in the list. Same here: 4826 digits. Last fiddled with by kar_bon on 2019-07-22 at 14:11

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2019-07-20, 20:12	#265
kar_bon Mar 2006 Germany 2908₁₀ Posts	Yes, the "date" "before November 4, 2018" in FactorDB was created after server/database moving by Markus, so not available older dates here. The list of Leyeland primes contains also some dates like for x=1031-1050 as reserved/complete, that's why I used "2001-06-04" for those 4 primes then. For other dates expressions like "2002-06" is enough here as you gave for >#294 in your list. Dates from your and Norberts finds should be better than. Will see how this can be handled. The great advantage of the table is the individual sorting: I tried first to sort by x-value in the category by the template, but this needed a click to sort the table by digits. Now it's done by sorting by digits and calling the table only. Inserting a new number you don't need to create an index (first column), it's done in the table call. Also: Clicking on "Digits" column first (upwards sorting) and than on "Prover" the smallest unproven number are listed in descending digit order: could be helpful to prove some smaller numbers. ToDo's: pages with information about those numbers, links, stats, current work/reservation, minus-side.

2019-07-23, 11:42	#268
NorbSchneider "Norbert" Jul 2014 Budapest 109 Posts	I found 3 new PRPs: 634^42803+42803^634, 119938 digits, 736^44335+44335^736, 127104 digits, 9946^17491+17491^9946, 69923 digits.

2019-07-24, 11:14	#269
kar_bon Mar 2006 Germany 2²×727 Posts	Those three new ones are in the Wiki, too. Some notes: - I'm using a date of discovery for old Leyland primes according to the "When completed" listed here. So listing/sorting in the table is available for those, too. - Primes with missing certificate in FactorDB are marked with a remark in the page and listed as orange in column "Prover" in the table. These certs should be inserted later. - I've found some certs. in FactorDB but not yet listed in pxp's list. I used the date and info of program from FactorDB. - I've inserted some discovery dates for numbers found during doublechecking from here. - Categories for proven and PRPs numbers available now. More to come.

2019-07-24, 17:30	#271
Dylan14 "Dylan" Mar 2017 3×193 Posts	Reserving the range x = 20001-30000, y = 801-1000.

2019-07-27, 16:58	#275
NorbSchneider "Norbert" Jul 2014 Budapest 109 Posts	Another new PRP: 746^44541+44541^746, 127955 digits.