Leyland Primes (x^y+y^x primes) - Page 46

lghu · 2022-04-23, 10:29

Next PRP:
101542^92885+92885^101542, 504465 digit, index: 6185645908
PRPtop confirmation OK.

pxp · 2022-04-23, 16:02

Quote:

Originally Posted by lghu

Next PRP:
101542^92885+92885^101542, 504465 digit, index: 6185645908
PRPtop confirmation OK.

Thanks. The number of digits is 504456 of course.

lghu · 2022-04-28, 16:15

Quote:

Originally Posted by pxp

Thanks. The number of digits is 504456 of course.

YES. Thank you. It's my copy error.

xilman · 2022-05-08, 20:06

Quote:

Originally Posted by pxp

Congratulations to Miklos. By the way, my list of all known Leyland primes tries hard to stay up-to-date but I will calculate an associated Leyland number index (the prime's position in OEIS sequence A076980) before I post a new entry. For these large numbers this takes me about 24 hours. I recently attempted to interest the Mathematica community in speeding up the program that I wrote to do this but have had no such improvement.

Has

Code:

 300     5829184   10133    (3178,1543)    Alexander Kuzmich    Oct 2001

still not been proven prime?

If so, I may give it a whirl through the latest ECPP release.

pxp · 2022-05-08, 21:19

Quote:

Originally Posted by xilman

Has

Code:

 300     5829184   10133    (3178,1543)    Alexander Kuzmich    Oct 2001

still not been proven prime?

If so, I may give it a whirl through the latest ECPP release.

Not as far as I know. Go for it!

xilman · 2022-05-09, 08:44

Quote:

Originally Posted by pxp

Not as far as I know. Go for it!

Thanks. I did.

The mpi processes crashed overnight for unexplained reasons but I suspect the system ran out of memory. Now to see whether a restart works as advertised ...

pxp · 2022-05-09, 10:08

I have now finished testing the Leyland numbers in the interval from L(303999,10) to L(304999,10) and have found therein 10 PRPs. That completes the fifth and final part of finding all PRPs in the interval L(299999,10) to L(304999,10). I have therein 63 PRPs, one of which is Anatoly Selevich's L(314738,9) found back in February 2011. I started the project on May 31 of last year, testing 1186439 sieved-to-10^10 candidates, manually distributed across (mostly) 72 Mac-mini cores, only taking some time out in August to add L(83747,41272) and L(80565,62824).

xilman · 2022-05-09, 15:05

Quote:

Originally Posted by xilman

Thanks. I did.

The mpi processes crashed overnight for unexplained reasons but I suspect the system ran out of memory. Now to see whether a restart works as advertised ...

Given that all the ecmclient processes also terminated but Linux did not I now believe it was memory exhaustion.

Now as far along as

Code:

-- Size [11]: 33084 bits
   Time for discriminant  -744891: 2732.0 (556.9)
   largest prime of d: 449
   largest prime of h: 11
       discriminants: 8.3 (9.0)
     1385 qroot:      6230.7 (1329.4)
  2395689 Cornacchia: 13309.0 (2787.3)
    37864 trial div:  2528.1 (442.3)
     9211 is_prime:   41706.0 (8859.6)
-- Size [12]: 33026 bits

Looks like it might be quite a while yet, but that is what I expect for a >10K digit prime candidate.

frmky · 2022-05-10, 18:32

I'll give (3042,2231) a go. I think it should take only a few hours on six 20-core nodes.

kruoli · 2022-05-10, 19:45

Quote:

Originally Posted by frmky

I'll give (3042,2231) a go. I think it should take only a few hours on six 20-core nodes.

Not a good idea...

Quote:

Originally Posted by kruoli

Reserving L(3042, 2231). Let's give fastECPP a try!

frmky · 2022-05-10, 20:08

Quote:

Originally Posted by kruoli

Not a good idea...

Oops, I missed that. I'll do (3594,697) then.

2022-05-09, 10:08	#502
pxp Sep 2010 Weston, Ontario 326₈ Posts	I have now finished testing the Leyland numbers in the interval from L(303999,10) to L(304999,10) and have found therein 10 PRPs. That completes the fifth and final part of finding all PRPs in the interval L(299999,10) to L(304999,10). I have therein 63 PRPs, one of which is Anatoly Selevich's L(314738,9) found back in February 2011. I started the project on May 31 of last year, testing 1186439 sieved-to-10^10 candidates, manually distributed across (mostly) 72 Mac-mini cores, only taking some time out in August to add L(83747,41272) and L(80565,62824). Last fiddled with by pxp on 2022-05-09 at 10:17 Reason: wording

Similar Threads
Thread	Thread Starter	Forum	Replies	Last Post
Leyland Primes: ECPP proofs	Batalov	XYYXF Project	37	2022-05-17 05:32
Mersenne Primes p which are in a set of twin primes is finite?	carpetpool	Miscellaneous Math	3	2017-08-10 13:47
Distribution of Mersenne primes before and after couples of primes found	emily	Math	34	2017-07-16 18:44
On Leyland Primes	davar55	Puzzles	9	2016-03-15 20:55
possible primes (real primes & poss.prime products)	troels munkner	Miscellaneous Math	4	2006-06-02 08:35

2022-04-23, 10:29	#496
lghu Nov 2019 13 Posts	Next PRP: 101542^92885+92885^101542, 504465 digit, index: 6185645908 PRPtop confirmation OK.

2022-05-10, 18:32	#504
frmky Jul 2003 So Cal 3×787 Posts	I'll give (3042,2231) a go. I think it should take only a few hours on six 20-core nodes.