Leyland Primes (x^y+y^x primes)

[rogue]

Originally Posted by Batalov

Placeholder for x^y+y^x prime search reservations.

Contact XYYXF to reserve a range. Multisieve is one of the sieve programs capable of sieving this form.

Now if Paul would like to take the time to update his webpage...

...or someone else could take ownership.

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

[Batalov]

[20001-40000, 11-200] range is done. One PRP I had found two years ago, and now, the rest:

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

Submitted to PRP top, they will show up in a few days.

[Batalov]

Originally Posted by XYYXF

E.g. it's possible to take [15001-20000, 1001-2000].

Ok. Consider this range done, too. ;-)

[TimSorbet]

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

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

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.

[Batalov]

Originally Posted by XYYXF

OK, http://xyyxf.at.tut.by/primes.html#ranges 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].

Done.

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

[Batalov]

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

[Batalov]

Reserving [40001-330000, 11-17]

[XYYXF]

Why not ...20]?

[Batalov]

Because it is more 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]

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]

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