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-   -   Leyland Primes (x^y+y^x primes) (https://www.mersenneforum.org/showthread.php?t=19347)

 rogue 2014-05-13 23:53

[QUOTE=Batalov;373293]Placeholder for x[SUP]y[/SUP]+y[SUP]x[/SUP] prime search reservations.

Contact [URL="http://www.mersenneforum.org/member.php?u=1540"]XYYXF[/URL] to [URL="http://xyyxf.at.tut.by/primes.html#0"]reserve a range[/URL]. Multisieve is one of the sieve programs capable of sieving this form.[/QUOTE]

Now if Paul would like to take the time to update his [URL="http://www.leyland.vispa.com/numth/primes/xyyx.htm"]webpage[/URL]...

...or someone else could take ownership.

[COLOR="Blue"]EDIT (S.B.): That's exactly what Andrey did a few years ago: [url]http://xyyxf.at.tut.by/primes.html#0[/url][/COLOR]

 Batalov 2014-05-14 00:13

[20001-40000, 11-200] range is done. One PRP I had found two years ago, and now, the rest:
[CODE]11^36442+36442^11, 37951(decimal digits) (2012)
33^21262+21262^33, 32287
63^20018+20018^63, 36020
76^24787+24787^76, 46620
92^32907+32907^92, 64623
98^27819+27819^98, 55394
105^34684+34684^105, 70103
117^26870+26870^117, 55573
128^29007+29007^128, 61124
128^32001+32001^128, 67433
129^28468+28468^129, 60085
131^31870+31870^131, 67478
143^39070+39070^143, 84209
157^29934+29934^157, 65733
163^26530+26530^163, 58690
181^22300+22300^181, 50347
200^20373+20373^200, 46879
[/CODE]
Submitted to PRP top, they will show up in a few days.

 Batalov 2014-05-14 08:31

[QUOTE=XYYXF;373379]E.g. it's possible to take [15001-20000, 1001-2000].[/QUOTE]
Ok. Consider this range done, too. ;-)

 Mini-Geek 2014-05-14 12:16

FWIW, the result of sieving the range [12501-15000, 2001-15000] to 1657571 (which took a few hours on a core)

[url]https://www.dropbox.com/s/5plhnqg5hwqtbn8/xyyx.7z[/url]

As a rough estimate: 700,000 candidates (guess of how many will remain after sieving; currently 720,880 remaining) at 40 seconds (timings for PFGW tests ranged from 26 to 58 seconds) per candidate per core makes this range an 80 day job for a quad core Haswell. I don't want to make that much of a commitment right now, but someone can use my sieve file as a starting point. :smile:

 Batalov 2014-05-14 17:22

[QUOTE=XYYXF;373379]OK, [url]http://xyyxf.at.tut.by/primes.html#ranges[/url] is updated. But I still hope someone will decrease the number of steps y>10, y>200, y>1000, y>2000 :-)

E.g. it's possible to take [15001-20000, 1001-2000].[/QUOTE]
Done.
[CODE]1033^16254+16254^1033, 48992
1263^19898+19898^1263, 61712
1265^19732+19732^1265, 61211
1271^17368+17368^1271, 53913
1338^15377+15377^1338, 48076
1417^15754+15754^1417, 49647
1456^19909+19909^1456, 62976
1508^17691+17691^1508, 56230
1537^18832+18832^1537, 60012
1576^19021+19021^1576, 60821
1638^15437+15437^1638, 49620
1684^16495+16495^1684, 53219
1741^19546+19546^1741, 63345
1828^16589+16589^1828, 54113
1839^17156+17156^1839, 56008
1845^16636+16636^1845, 54334
1850^18879+18879^1850, 61681
1897^16710+16710^1897, 54777
1908^17605+17605^1908, 57755
1943^15222+15222^1943, 50058
[/CODE]

 Batalov 2014-05-15 15:49

And one PRP to rule them all:
15^328574+328574^15 (386434 digits) :smile:

 Batalov 2014-05-15 16:38

Reserving [40001-330000, 11-17]

 XYYXF 2014-05-15 19:54

Why not ...20]?

 Batalov 2014-05-15 20:36

Because it is [I]more[/I] work? ;-)
Maybe later.

(19 and 20 are particularly heavy and 20^330000 >> 17^330000)
Someone can relatively easily do the y=18. Free idea! Anyone?

 fivemack 2014-05-15 23:50

I am running Y=18, should make it to 300k by the end of the month unless I've screwed up my calculations somewhere.

 Batalov 2014-05-16 17:34

[40001-330000, 11-17] is done. Three PRPs:
11^255426+255426^11
12^47489+47489^12 (previously known)
15^328574+328574^15

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