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-   -   Leyland Primes: ECPP proofs (https://www.mersenneforum.org/showthread.php?t=19348)

 Batalov 2014-05-12 21:07

Leyland Primes: ECPP proofs

Placeholder for x[SUP]y[/SUP]+y[SUP]x[/SUP] prime proofs.
[url]http://www.primefan.ru/xyyxf/primes.html#0[/url]
There are some PRPs available starting from ~6600 digit size.

Contact [URL="http://www.mersenneforum.org/member.php?u=1540"]XYYXF[/URL] to reserve.

 Batalov 2014-05-12 21:17

There are a few existing reservations that make one very curious:
[I]222748^3+3^222748 (a 106278 decimal digits PRP by Anatoly Selevich) is reserved by Jens Franke.[/I]
Is it that the low value of y=3 makes for a very special case for a ECPP proof?

 XYYXF 2014-05-13 08:01

AFAIK, they're going to make a CIDE proof, as it was done for 8656^2929+2929^8656:

 henryzz 2014-05-13 10:00

[QUOTE=XYYXF;373341]AFAIK, they're going to make a CIDE proof, as it was done for 8656^2929+2929^8656:

Does anyone know whether this method has been peer reviewed/checked over yet? Is there an available implementation of this algorithm?

 RichD 2015-01-20 22:40

PRP Now Proven Prime

I completed several Primo proofs:

[url="http://factordb.com/index.php?id=1100000000537924327&open=prime"]2284^1985+1985^2284[/url]
[url="http://factordb.com/index.php?id=1100000000536776621&open=prime"]2305^1374+1374^2305[/url]
[url="http://factordb.com/index.php?id=1100000000536776641&open=prime"]2317^1354+1354^2317[/url]
[url="http://factordb.com/index.php?id=1100000000534878923&open=prime"]2328^923+923^2328[/url]
[url="http://factordb.com/index.php?id=1100000000534854226&open=prime"]2343^962+962^2343[/url]
[url="http://factordb.com/index.php?id=1100000000534870605&open=prime"]2383^1710+1710^2383[/url]

Two more will be completed this week.

2349^1772+1772^2349
2408^975+975^2408

 RichD 2015-01-24 14:31

[QUOTE=RichD;393006]Two more will be completed this week.

2349^1772+1772^2349
2408^975+975^2408[/QUOTE]

All done.

 XYYXF 2015-02-02 15:10

Thanks for the proofs :)

 RichD 2015-06-04 09:50

A few more Primo proofs:

[url="http://factordb.com/index.php?id=1100000000781133141&open=prime"]2613^2348+2348^2613[/url]
[url="http://factordb.com/index.php?id=1100000000781133133&open=prime"]2665^1702+1702^2665[/url]
[url="http://factordb.com/index.php?id=1100000000781133070&open=prime"]2685^1904+1904^2685[/url]
[url="http://factordb.com/index.php?id=1100000000781133089&open=prime"]2696^2451+2451^2696[/url]

 RichD 2016-01-08 04:12

A few more Primo proofs:

[url="http://factordb.com/index.php?id=1100000000809752661&open=prime"]2596^1867+1867^2596[/url]
[url="http://factordb.com/index.php?id=1100000000809752888&open=prime"]2622^2129+2129^2622[/url]
[url="http://factordb.com/index.php?id=1100000000809753326&open=prime"]2625^1094+1094^2625[/url]
[url="http://factordb.com/index.php?id=1100000000809753669&open=prime"]2680^2053+2053^2680[/url]
[url="http://factordb.com/index.php?id=1100000000809753913&open=prime"]2722^2445+2445^2722[/url]
[url="http://factordb.com/index.php?id=1100000000809753933&open=prime"]2759^2200+2200^2759[/url]

 CRGreathouse 2016-01-08 17:02

[QUOTE=henryzz;373345]Does anyone know whether this method has been peer reviewed/checked over yet? Is there an available implementation of this algorithm?[/QUOTE]

I wonder these things myself (many months later).

 XYYXF 2016-01-10 20:27

Thanks for the proofs :-)

The page is updated: [url]http://www.primefan.ru/xyyxf/primes.html#0[/url]

 RichD 2016-01-23 03:08

A few more Primo proofs:

[url="http://factordb.com/index.php?id=1100000000812836487&open=prime"]2771^2640+2640^2771[/url]
[url="http://factordb.com/index.php?id=1100000000812836497&open=prime"]2779^1632+1632^2779[/url]
[url="http://factordb.com/index.php?id=1100000000812836504&open=prime"]2779^2560+2560^2779[/url]

 XYYXF 2016-02-14 21:21

Thank you Rich.

 RichD 2017-06-16 03:04

Several more Primo proofs:

[url="http://factordb.com/index.php?id=1100000000936468038&open=prime"]2495^2424+2424^2495[/url]
[url="http://factordb.com/index.php?id=1100000000936468076&open=prime"]2528^2031+2031^2528[/url]
[url="http://factordb.com/index.php?id=1100000000936116882&open=prime"]2553^974+974^2553[/url]
[url="http://factordb.com/index.php?id=1100000000936116954&open=prime"]2573^1134+1134^2573[/url]

 RichD 2017-07-30 16:43

Yet a few more Primo proofs.
I believe this completes all PRPs where x<2800.

[url="http://factordb.com/index.php?id=1100000000537925843&open=prime"]2448^535+535^2448[/url]
[url="http://factordb.com/index.php?id=1100000000537925880&open=prime"]2453^2094+2094^2453[/url]
[url="http://factordb.com/index.php?id=1100000000537925889&open=prime"]2460^671+671^2460[/url]
[url="http://factordb.com/index.php?id=1100000000537925894&open=prime"]2463^1274+1274^2463[/url]
[url="http://factordb.com/index.php?id=1100000000537926175&open=prime"]2470^1249+1249^2470[/url]
[url="http://factordb.com/index.php?id=1100000000939418216&open=prime"]2473^1188+1188^2473[/url]
[url="http://factordb.com/index.php?id=1100000000939395721&open=prime"]2481^2432+2432^2481[/url]
[url="http://factordb.com/index.php?id=1100000000939419263&open=prime"]2489^1858+1858^2489[/url]
[url="http://factordb.com/index.php?id=1100000000536776629&open=prime"]2494^635+635^2494[/url]
[url="http://factordb.com/index.php?id=1100000000936116856&open=prime"]2522^537+537^2522[/url]
[url="http://factordb.com/index.php?id=1100000000939419962&open=prime"]2543^414+414^2453[/url]
[url="http://factordb.com/index.php?id=1100000000813529235&open=prime"]2675^298+298^2675[/url]

 RichD 2017-10-29 00:05

A few more Primo proofs.
This should complete all PRPs where x<3000.

[url=http://factordb.com/index.php?id=1100000000936469430&open=prime]2803^916+916^2803[/url]
[url=http://factordb.com/index.php?id=1100000000936469499&open=prime]2823^836+836^2823[/url]
[url=http://factordb.com/index.php?id=1100000000936469517&open=prime]2826^1289+1289^2826[/url]
[url=http://factordb.com/index.php?id=1100000000572260258&open=prime]2831^666+666^2831[/url]
[url=http://factordb.com/index.php?id=1100000000676169466&open=prime]2843^208+208^2843[/url]
[url=http://factordb.com/index.php?id=1100000000936469590&open=prime]2883^1136+1136^2883[/url]
[url=http://factordb.com/index.php?id=1100000000936469604&open=prime]2890^1671+1671^2890[/url]
[url=http://factordb.com/index.php?id=1100000000936469613&open=prime]2892^2035+2035^2892[/url]
[url=http://factordb.com/index.php?id=1100000000936469627&open=prime]2974^2735+2735^2974[/url]
[url=http://factordb.com/index.php?id=1100000000936469650&open=prime]2987^2680+2680^2987[/url]
[url=http://factordb.com/index.php?id=1100000000936469695&open=prime]2996^1563+1563^2996[/url]

 Dylan14 2019-08-04 00:32

It's been a while since I've seen a primality proof of a Leyland number here, so to rectify that, earlier today I did the proof of 214^3147+3147^214: [URL]http://factordb.com/index.php?id=1100000000420123164[/URL]

 kruoli 2021-07-12 20:05

Whoops, I just saw this thread here. If wished for, would you please move my posts with the proof reservations from the other thread here?

 kruoli 2021-07-20 16:36

All Leyland primes below 10,000 digits are now certified in FactorDB; my reservations are completed. For now, I will not reserve anything new.

 xilman 2021-07-20 21:07

[QUOTE=kruoli;583598]All Leyland primes below 10,000 digits are now certified in FactorDB; my reservations are completed. For now, I will not reserve anything new.[/QUOTE]:tu:

 kruoli 2021-11-07 20:36

When I just checked Prime Wiki, there were still three numbers below 10,000 digits that have no certificate on FactorDB. I must have overlooked them, I guess? I will rectify this omission soon. Also, I will add certificates for the next three numbers that do not have a certificate yet after that. For the next year, my goal is to have all up to 12,500 digits certified. Any help for this endeavour is appreciated. But beside the six numbers mentioned above, it will be some time until I start this.

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