Leyland Primes (x^y+y^x primes) - Page 22

NorbSchneider · 2017-03-24, 11:15

I reached x=30,000 and found 2 new PRPs:
474^27863+27863^474, 74556 digits,
536^29847+29847^536, 81458 digits.

pxp · 2017-04-27, 20:31

I have now finished with the Leyland numbers in the gap between L(40495,114) <83295 digits> and L(35917,214) <83702 digits> and have found therein 6 new PRPs:

L(20850,9971) <83374>
L(20519,11572) <83378>
L(21368,8085) <83500>
L(26870,1293) <83609>
L(19522,19283) <83656>
L(20091,14596) <83664>

NorbSchneider · 2017-05-30, 12:55

I reached x=31,000 and found 3 new PRPs:
734^30453+30453^734, 87270 digits,
423^30634+30634^423, 80456 digits,
758^30693+30693^758, 88386 digits.

pxp · 2017-06-30, 07:38

I have now finished with the Leyland numbers in the gap between L(35917,214) <83702 digits> and L(39070,143) <84209 digits> and have found therein 7 new PRPs:

L(23543,3610) <83755>
L(20625,11522) <83770>
L(19551,19268) <83773>
L(21457,8200) <83979>
L(21234,9067) <84033>
L(20996,10059) <84038>
L(21485,8224) <84116>

NorbSchneider · 2017-07-24, 10:18

I reached x=32,000 and found 1 new PRP:
496^31671+31671^496, 85369 digits.

pxp · 2018-04-01, 14:14

I'm looking for the date of discovery of Anatoly Selevich's L(8656,2929) <30008 digits>. This number went on to be proven prime, which may have been why it wasn't in PRPtop when I added it on his behalf in Aug. 2015. For the record, I have eight other Leyland primes with more than 10000 decimal digits for which I don't have a discovery date:

<10041> L(3571,648) Paul Leyland
<10073> L(2930,2739) Greg Childers
<10094> L(3265,1234) Leonid Muraviov
<13740> L(5140,471) Paul Leyland
<15071> L(4405,2638) Greg Childers
<16868> L(5182,1799) Paul Leyland
<17283> L(5154,2255) Paul Leyland
<18195> L(5155,3384) Paul Leyland

If anyone can reference a discovery date for any of these, I'd be very grateful.

pxp · 2018-04-01, 14:52

There are currently 1000 Leyland primes listed in PRPtop. Since my currently known number is 1302, we therefore have 302 missing: 128 (from Paul Leyland), 54 (Andrey Kulsha), 52 (Greg Childers), 25 (Peter Liaskovsky), 23 (Christ van Willegen), 5 (Alexander Kuzmich), 4 (Rob Binnekamp), 3 (Leonid Muraviov), 2 (each, from Mark Rodenkirch, Henri Lifchitz, Göran Hemdal, & Sander Hoogendoorn). My (Hans Havermann) PRPtop Leyland prime listing includes 6 that are actually from "firejuggler".

There are 1250 Leyland primes in Andrey Kulsha's Jan. 2017 list. The missing 52 are accounted for by discoveries from me (44) and Norbert Schneider (8).

My ongoing Leyland prime indexing effort is here.

xilman · 2018-04-01, 16:34

Quote:

Originally Posted by pxp

I'm looking for the date of discovery of Anatoly Selevich's L(8656,2929) <30008 digits>. This number went on to be proven prime, which may have been why it wasn't in PRPtop when I added it on his behalf in Aug. 2015. For the record, I have eight other Leyland primes with more than 10000 decimal digits for which I don't have a discovery date:

<10041> L(3571,648) Paul Leyland
<10073> L(2930,2739) Greg Childers
<10094> L(3265,1234) Leonid Muraviov
<13740> L(5140,471) Paul Leyland
<15071> L(4405,2638) Greg Childers
<16868> L(5182,1799) Paul Leyland
<17283> L(5154,2255) Paul Leyland
<18195> L(5155,3384) Paul Leyland

If anyone can reference a discovery date for any of these, I'd be very grateful.

It's just about possible, though unlikely, I may be able to find the information for the ones I discovered. It will require digging through decade-old material from when I worked for MSRC. All will be between (roughly) 2000 and 2005.

Paul

pxp · 2018-04-02, 19:31

I believe that I can construct reasonable discovery dates for all but Anatoly Selevich's L(8656,2929) by using Paul's ranges-being-searched table. Obviously the date will fall between when-reserved and when-completed in roughly the same proportion as x falls between xmin and xmax. That leaves L(8656,2929) as being discovered after Oct. 2006, since this number is not yet in Paul's primes-and-strong-pseudoprimes list.

pxp · 2018-04-02, 21:57

I've put Selevich's Leyland prime output from Aug 2007 through Jan 2008 (as dated in PRPtop) here. It seems that (8656,2929) should fall somewhere in this date-range but it isn't obvious to me what's going on. He was likely searching different (x,y)-ranges on different processors.

pxp · 2018-06-01, 14:11

The odds of finding a d-digit Leyland prime where d ~ 100000 are (empirically) about 1 in 75. In other words, one should expect to find about 40 Leyland primes with digit-size ranging from 100000 to 103000. What are the odds when d ~ 400000 ?

2018-04-02, 19:31	#240
pxp Sep 2010 Weston, Ontario 2³·5² Posts	I believe that I can construct reasonable discovery dates for all but Anatoly Selevich's L(8656,2929) by using Paul's ranges-being-searched table. Obviously the date will fall between when-reserved and when-completed in roughly the same proportion as x falls between xmin and xmax. That leaves L(8656,2929) as being discovered after Oct. 2006, since this number is not yet in Paul's primes-and-strong-pseudoprimes list. Last fiddled with by pxp on 2018-04-02 at 19:55 Reason: clarification

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2017-03-24, 11:15	#232
NorbSchneider "Norbert" Jul 2014 Budapest 1101101₂ Posts	I reached x=30,000 and found 2 new PRPs: 474^27863+27863^474, 74556 digits, 536^29847+29847^536, 81458 digits.

2017-04-27, 20:31	#233
pxp Sep 2010 Weston, Ontario 2³·5² Posts	I have now finished with the Leyland numbers in the gap between L(40495,114) <83295 digits> and L(35917,214) <83702 digits> and have found therein 6 new PRPs: L(20850,9971) <83374> L(20519,11572) <83378> L(21368,8085) <83500> L(26870,1293) <83609> L(19522,19283) <83656> L(20091,14596) <83664>

2017-05-30, 12:55	#234
NorbSchneider "Norbert" Jul 2014 Budapest 109 Posts	I reached x=31,000 and found 3 new PRPs: 734^30453+30453^734, 87270 digits, 423^30634+30634^423, 80456 digits, 758^30693+30693^758, 88386 digits.

2017-06-30, 07:38	#235
pxp Sep 2010 Weston, Ontario 310₈ Posts	I have now finished with the Leyland numbers in the gap between L(35917,214) <83702 digits> and L(39070,143) <84209 digits> and have found therein 7 new PRPs: L(23543,3610) <83755> L(20625,11522) <83770> L(19551,19268) <83773> L(21457,8200) <83979> L(21234,9067) <84033> L(20996,10059) <84038> L(21485,8224) <84116>

2017-07-24, 10:18	#236
NorbSchneider "Norbert" Jul 2014 Budapest 109 Posts	I reached x=32,000 and found 1 new PRP: 496^31671+31671^496, 85369 digits.

2018-04-01, 14:14	#237
pxp Sep 2010 Weston, Ontario C8₁₆ Posts	I'm looking for the date of discovery of Anatoly Selevich's L(8656,2929) <30008 digits>. This number went on to be proven prime, which may have been why it wasn't in PRPtop when I added it on his behalf in Aug. 2015. For the record, I have eight other Leyland primes with more than 10000 decimal digits for which I don't have a discovery date: <10041> L(3571,648) Paul Leyland <10073> L(2930,2739) Greg Childers <10094> L(3265,1234) Leonid Muraviov <13740> L(5140,471) Paul Leyland <15071> L(4405,2638) Greg Childers <16868> L(5182,1799) Paul Leyland <17283> L(5154,2255) Paul Leyland <18195> L(5155,3384) Paul Leyland If anyone can reference a discovery date for any of these, I'd be very grateful.

2018-04-01, 14:52	#238
pxp Sep 2010 Weston, Ontario 2³·5² Posts	There are currently 1000 Leyland primes listed in PRPtop. Since my currently known number is 1302, we therefore have 302 missing: 128 (from Paul Leyland), 54 (Andrey Kulsha), 52 (Greg Childers), 25 (Peter Liaskovsky), 23 (Christ van Willegen), 5 (Alexander Kuzmich), 4 (Rob Binnekamp), 3 (Leonid Muraviov), 2 (each, from Mark Rodenkirch, Henri Lifchitz, Göran Hemdal, & Sander Hoogendoorn). My (Hans Havermann) PRPtop Leyland prime listing includes 6 that are actually from "firejuggler". There are 1250 Leyland primes in Andrey Kulsha's Jan. 2017 list. The missing 52 are accounted for by discoveries from me (44) and Norbert Schneider (8). My ongoing Leyland prime indexing effort is here.

2018-04-02, 21:57	#241
pxp Sep 2010 Weston, Ontario 310₈ Posts	I've put Selevich's Leyland prime output from Aug 2007 through Jan 2008 (as dated in PRPtop) here. It seems that (8656,2929) should fall somewhere in this date-range but it isn't obvious to me what's going on. He was likely searching different (x,y)-ranges on different processors.

2018-06-01, 14:11	#242
pxp Sep 2010 Weston, Ontario 200₁₀ Posts	The odds of finding a d-digit Leyland prime where d ~ 100000 are (empirically) about 1 in 75. In other words, one should expect to find about 40 Leyland primes with digit-size ranging from 100000 to 103000. What are the odds when d ~ 400000 ?