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

[pxp]

Originally Posted by storm5510

Attached is a snip from pxp's current table. There is a gap between the two highlighted areas. Has any of this been tested? I am looking for something to run.

Gaps in my current table generally represent untested numbers. However, in this instance I will have finished looking at candidates up to 386700 digits by next week, so far without a find. I had no intention of looking beyond that.

[storm5510]

Originally Posted by pxp

Gaps in my current table generally represent untested numbers. However, in this instance I will have finished looking at candidates up to 386700 digits by next week, so far without a find. I had no intention of looking beyond that.

Thank you for your reply. I wasn't sure I would get one.

Very well. I will just let this go then.

[pxp]

Originally Posted by paulunderwood

Congrats to frmky for the proof of 3^78296+78296^3 with 37,357 decimal digits

That took factordb 17 days to verify!

[NorbSchneider]

Another new PRP:
20596^40995+40995^20596, 176844 digits.

[NorbSchneider]

Another new PRP:
20530^41031+41031^20530, 176942 digits.

[NorbSchneider]

Another new PRP:
32363^33292+33292^32363, 150149 digits.

[japelprime]

I am keen on sieve from the Leyland first kind (plus form) table a (x,Y) range
(15001,2000) to (20000,19999).
https://www.rieselprime.de/ziki/Leyland_number

Is this ok or am I tresspassing others job here ?

[pxp]

Originally Posted by japelprime

I am keen on sieve from the Leyland first kind (plus form) table a (x,Y) range (15001,2000) to (20000,19999).

The largest Leyland number in your range is 86021 decimal digits. It has been claimed that all Leyland primes smaller than 150000 decimal digits are known. See my table of Leyland primes here. To generate a 150000-digit (or larger) Leyland number, x can not be smaller than 33180.

[japelprime]

Originally Posted by pxp

The largest Leyland number in your range is 86021 decimal digits. It has been claimed that all Leyland primes smaller than 150000 decimal digits are known. See my table of Leyland primes here. To generate a 150000-digit (or larger) Leyland number, x can not be smaller than 33180.

Ok. So it is maybe not organized as a project any more who is doing different range any more?

Thanks.

[pxp]

Originally Posted by japelprime

Ok. So it is maybe not organized as a project any more who is doing different range any more?

That is essentially correct. But I will point out that this doesn't prevent people from finding and contributing new Leyland primes. So far this calendar year there have been 36 new Leyland primes added by four different contributors. The third column is the number of decimal digits:

Hans Havermann     Jan 2022  303129  (80160,6047) 
Hans Havermann     Jan 2022  303285  (71016,18649)
Hans Havermann     Jan 2022  303343  (65018,46293)
Hans Havermann     Jan 2022  303580  (78390,7459) 
Hans Havermann     Jan 2022  303724  (66094,39385)
Hans Havermann     Jan 2022  303782  (80766,5771) 
Hans Havermann     Jan 2022  303989  (77842,8039) 
Gabor Levai        Jan 2022  500027 (101070,88579)
Hans Havermann     Feb 2022  303063  (65537,42102)
Hans Havermann     Feb 2022  303492  (65008,46615)
Hans Havermann     Feb 2022  303589  (69147,24574)
Hans Havermann     Feb 2022  303906  (67389,32338)
Hans Havermann     Feb 2022  303935  (64209,54140)
Hans Havermann     Feb 2022  303998  (74442,12125)
Hans Havermann     Feb 2022  304818  (65473,45250)
Miklos Levai       Feb 2022  506429 (107890,49423)
Norbert Schneider  Mar 2022  162498  (62093,414)  
Hans Havermann     Mar 2022  303094  (67434,31237)
Hans Havermann     Mar 2022  304222  (84473,3994) 
Hans Havermann     Mar 2022  304336  (70170,21733)
Hans Havermann     Mar 2022  304403  (71729,17530)
Hans Havermann     Mar 2022  304487  (64492,52639)
Hans Havermann     Mar 2022  304569 (238176,19)   
Hans Havermann     Mar 2022  304794  (66012,41423)
Gabor Levai        Mar 2022  500126 (101761,82168)
Hans Havermann     Apr 2022  304437  (65955,41288)
Hans Havermann     Apr 2022  304742  (65073,48202)
Gabor Levai        Apr 2022  504456 (101542,92885)
Norbert Schneider  May 2022  172338  (37674,37535)
Hans Havermann     May 2022  304539  (73122,14615)
Gabor Levai        May 2022 1000027 (211185,54364)
Norbert Schneider  Jun 2022  173562  (37916,37803)
Norbert Schneider  Jun 2022  196083 (129128,33)   
Norbert Schneider  Jul 2022  150149  (33292,32363)
Norbert Schneider  Jul 2022  176844  (40995,20596)
Norbert Schneider  Jul 2022  176942  (41031,20530)

[japelprime]

Thanks for the info.
I do not want to do uncontrolled Sieve range or solo work out of the blue here. To messy. Any gabs to close maybe if that will help ?