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.

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?

AFAIK, they're going to make a CIDE proof, as it was done for 8656^2929+2929^8656:
[url]http://www.mersenneforum.org/showthread.php?t=17554[/url]

[QUOTE=XYYXF;373341]AFAIK, they're going to make a CIDE proof, as it was done for 8656^2929+2929^8656:
[URL]http://www.mersenneforum.org/showthread.php?t=17554[/URL][/QUOTE]

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

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

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

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

All done.

Thanks for the proofs :)

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]

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]

[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).

Thanks for the proofs :-)

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

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]

Thank you Rich.

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]

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]

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]

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]

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?