Leyland Primes (x^y+y^x primes) - Page 11

pxp · 2016-01-06, 09:14

Today I found probable prime Leyland(12876,2447) — which was surprising because it should have been covered by XYYXF's reservation scheme. The slightly larger L(12617,2880) is currently being credited to me (presumably because I submitted some missing entries to the PRP-records site on behalf of others) but it was actually found by "firejuggler". I note also a previous confusion about the lower bound of y in L(x,y). Regardless, I am not taking anything for granted and my from-scratch recalculation of the smallest Leyland primes should reach L(12876,2447) in another two-and-a-half weeks. I have already diverted most of my resources to exploring subsequent intervals (between known Leyland primes).

XYYXF · 2016-01-10, 16:38

Quote:

Originally Posted by pxp

Today I found probable prime Leyland(12876,2447) — which was surprising because it should have been covered by XYYXF's reservation scheme.

That's an old leak: http://www.mersenneforum.org/showpos...1&postcount=94

I'm slowly covering that window now...

NorbSchneider · 2016-01-27, 11:13

I reached x=12,800 and found 2 new PRPs:
9328^12787+12787^9328, 50762 digits,
11542^12787+12787^11542, 51945 digits.

pxp · 2016-01-28, 23:29

I have another five finds: L(13051,2448), L(13227,2200), L(13307,3442), L(13343,3150), and L(13371,3068). My indexing-the-Leyland-primes project is now complete to L(11200,9267) which is #969 in OEIS A094133 [where L(3,2) is #2]. I hope to know #1000 by summer.

pxp · 2016-02-06, 10:01

My Leyland primes list is now indexed to #986 L(12357,4862). The bottleneck to #1000 will be the gap between L(11572,9463) and L(12172,6713) which I will examine starting in two weeks. By distributing the search between four processors, I hope to complete it by the end of March.

XYYXF · 2016-02-13, 01:14

(13896,2119) is also a PRP.

XYYXF · 2016-02-14, 17:46

Quote:

Originally Posted by XYYXF

Now it would be nice to fill the gap 2000 < x <= 2500 for 12500 < y <= 15000 :-)

The gap is filled with (14254,2227) and (14734,2397).

Hans, please check the updated page: http://www.primefan.ru/xyyxf/primes.html#0

pxp · 2016-02-15, 18:00

Quote:

Originally Posted by XYYXF

Hans, please check the updated page: http://www.primefan.ru/xyyxf/primes.html#0

Looks good. I see you picked up the three I had found earlier this month. One more today: L(13693,5212). I started the "bottleneck" gap mentioned in my last message. I'll have the next significant indexing update by mid-March.

pxp · 2016-03-07, 12:31

My indexing is now up to #1022 L(14254,2227).

XYYXF · 2016-03-07, 18:55

New PRPs are:
(13024,3285)
(13167,3436)
(13284,3335)
(12855,5032) - should be already found by Norbert
(13693,5212)
(13292,6867)

Right? :-)

NorbSchneider · 2016-03-07, 21:55

I reached x=12,865 and found no new PRPs.
I found (12855,5032) later than Hans Havermann,
also he is the discoverer.

I found 2 more PRPs on prptop, discovered by Hans Havermann.
12943^6574+6574^12943, 49415 digits,
14038^4327+4327^14038, 51045 digits.

I search also PRPs of the form y^x-x^y.
I made a webpage to these PRPs, similar to Andrey's page
to the y^x+x^y PRPs. You can find the page at primfakt.atw.hu,
y^x-x^y PRPs exists much more than y^x+x^y PRPs.
For example to x= 5000 894 y^x-x^y and 426 y^x+x^y PRPs,
x=10000 1530 y^x-x^y and 787 y^x+x^y PRPs.
I have all the y^x-x^y PRPs to x=10800, and a few for higher x values.
Andrey, Hans or someone else, are you interesting to join me
searching the y^x-x^y PRPs?

2016-03-07, 18:55	#120
XYYXF Jan 2005 Minsk, Belarus 2⁴·5² Posts	New PRPs are: (13024,3285) (13167,3436) (13284,3335) (12855,5032) - should be already found by Norbert (13693,5212) (13292,6867) Right? :-) Last fiddled with by XYYXF on 2016-03-07 at 19:48

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2016-01-06, 09:14	#111
pxp Sep 2010 Weston, Ontario 2³×5² Posts	Today I found probable prime Leyland(12876,2447) — which was surprising because it should have been covered by XYYXF's reservation scheme. The slightly larger L(12617,2880) is currently being credited to me (presumably because I submitted some missing entries to the PRP-records site on behalf of others) but it was actually found by "firejuggler". I note also a previous confusion about the lower bound of y in L(x,y). Regardless, I am not taking anything for granted and my from-scratch recalculation of the smallest Leyland primes should reach L(12876,2447) in another two-and-a-half weeks. I have already diverted most of my resources to exploring subsequent intervals (between known Leyland primes).

2016-01-27, 11:13	#113
NorbSchneider "Norbert" Jul 2014 Budapest 109 Posts	I reached x=12,800 and found 2 new PRPs: 9328^12787+12787^9328, 50762 digits, 11542^12787+12787^11542, 51945 digits.

2016-01-28, 23:29	#114
pxp Sep 2010 Weston, Ontario 2³×5² Posts	I have another five finds: L(13051,2448), L(13227,2200), L(13307,3442), L(13343,3150), and L(13371,3068). My indexing-the-Leyland-primes project is now complete to L(11200,9267) which is #969 in OEIS A094133 [where L(3,2) is #2]. I hope to know #1000 by summer.

2016-02-06, 10:01	#115
pxp Sep 2010 Weston, Ontario 2³·5² Posts	My Leyland primes list is now indexed to #986 L(12357,4862). The bottleneck to #1000 will be the gap between L(11572,9463) and L(12172,6713) which I will examine starting in two weeks. By distributing the search between four processors, I hope to complete it by the end of March.

2016-02-13, 01:14	#116
XYYXF Jan 2005 Minsk, Belarus 2⁴·5² Posts	(13896,2119) is also a PRP.

2016-03-07, 12:31	#119
pxp Sep 2010 Weston, Ontario 2³·5² Posts	My indexing is now up to #1022 L(14254,2227).

2016-03-07, 21:55	#121
NorbSchneider "Norbert" Jul 2014 Budapest 109 Posts	I reached x=12,865 and found no new PRPs. I found (12855,5032) later than Hans Havermann, also he is the discoverer. I found 2 more PRPs on prptop, discovered by Hans Havermann. 12943^6574+6574^12943, 49415 digits, 14038^4327+4327^14038, 51045 digits. I search also PRPs of the form y^x-x^y. I made a webpage to these PRPs, similar to Andrey's page to the y^x+x^y PRPs. You can find the page at primfakt.atw.hu, y^x-x^y PRPs exists much more than y^x+x^y PRPs. For example to x= 5000 894 y^x-x^y and 426 y^x+x^y PRPs, x=10000 1530 y^x-x^y and 787 y^x+x^y PRPs. I have all the y^x-x^y PRPs to x=10800, and a few for higher x values. Andrey, Hans or someone else, are you interesting to join me searching the y^x-x^y PRPs?