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Old 2008-07-24, 03:04   #166
robert44444uk
 
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Jun 2003
Suva, Fiji

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Quote:
Originally Posted by roger View Post
I figured out the A-value for the y=A*n^2, but I got a different answer than the 0.24 as suggested earlier.
Roger, back after a lot of travelling. How did you calculate your values? The 0.24 conjecture is the median value over sets of 50 consecutive n values with almost all A in the range 50% -200% of the conjected 0.24
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Old 2008-07-24, 20:23   #167
roger
 
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Oct 2006

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I took the trendline values of 0.3008*n^1.9545 to calculate the y-value for n=1.9545, then divided that y-value by the squared n-value (of k*2^n+-1).

Here's the steps I took in case I made an error:

y=0.3008*n1.9545
y=A*n2
A*n2 = 0.3008*n1.9545
[0.3008*n1.9545]/n2 = A

I used the last line of calculation on each n-value in k*2^n+-1, to come up with an A-value for each n-value in the curve A*n2.

The last data point (n=8000; the found twins) has an A-value of 0.19984.

I think I did something different than you though, because my values don't vary too much, they just follow an almost straight line (I posted the graph, and every thousand or so A-values a couple replies back).
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Old 2008-07-25, 04:08   #168
robert44444uk
 
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Jun 2003
Suva, Fiji

2·1,021 Posts
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Quote:
Originally Posted by roger View Post
I took the trendline values of 0.3008*n^1.9545 to calculate the y-value for n=1.9545, then divided that y-value by the squared n-value (of k*2^n+-1).

Here's the steps I took in case I made an error:

y=0.3008*n1.9545
y=A*n2
A*n2 = 0.3008*n1.9545
[0.3008*n1.9545]/n2 = A

I used the last line of calculation on each n-value in k*2^n+-1, to come up with an A-value for each n-value in the curve A*n2.

The last data point (n=8000; the found twins) has an A-value of 0.19984.

I think I did something different than you though, because my values don't vary too much, they just follow an almost straight line (I posted the graph, and every thousand or so A-values a couple replies back).
OK, understood, but don't think valid, as the best fit is arbitrary.
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Old 2008-08-01, 05:40   #169
roger
 
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Oct 2006

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Could the program we're using be modified slightly to do a large number of isolated k-values, for a large range of n-values?

I'm also trying to do the 100 primes by n=10,000 thing, and I think this would speed things up quite a bit for the higher n-values. The payam-base program could do the first 1000 or 2000 n-values, and spit out the k's that made it through. These would go to pfgw for n=1000 or 2000-5000, and the remaining would go through the modified cllr and .bat files we're using here. It would be a lot more efficient than pfgw-testing the ones payam-base spits out to n=5000, then sieving for each of those to n=10000.

Also, is there a way to get the .bat files to only output the primes that it's found? It would save me a lot of time as well I'm guessing it would be a modification of this line:

DO @echo %%j %%i >>all_twins.txt

Thanks!
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Old 2008-08-23, 10:08   #170
roger
 
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8000<n<8825 is done which makes for 95% of the first 10000 n-values complete :yay:

I think I'll finish off the 9500<n<10000, then just work on individual n-values.

Update on individual n-value search:

Code:
n=	done to	k= (Millions)	Primes in range
				
33200	227.9			
34528	56.5			
34543	5			12
40000	0.74			
40001	5.75			
40002	20			
40003	10.68			2
40004	50			49
40011	5			
40012	5			
40013	5			
45321	5			5
50000	1.17			1
50001	1			1
50002	1			
50003	2			1
50004	1M<k<3M			1
50005	7.53			9
57557	5			5
59729	5			5
59747	18.83			16
59753	5			1
59771	5			3
61855	1			1
62627	30			35
63337	5			3
67777	5			4
70207	5			1
71899	5			4
72727	10			8
73237	5			3
75000	100			106
75075	34.05			36
Code:
8000		5305077
8001		116835
8002		13267893
8003		7628139
8004		32708637
8005		19565691
8006		43954287
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roger is offline   Reply With Quote
Old 2008-09-12, 10:50   #171
kar_bon
 
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Mar 2006
Germany

2×1,531 Posts
Default

updated the page with first twin-k with new data (from roger upto n=9500) and new images.
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Old 2008-11-30, 07:01   #172
roger
 
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Oct 2006

22·5·13 Posts
Default

5 more n's to find twins for, then we're done to n=10,000!

I think this milestone deserves a

Will post full excel document (2MB) once completed.
It includes a lowest twin graph (logarithmic); deviation from mean (min/max); jumping champions (68 so far); average twin k-value; A-value for curve=A*2^n (at n=10000 A=0.20206).

After this, I will work on some higher n-values (in the range of 50k-80k I think) and may help more in smaller chunks to further this search.
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Old 2008-11-30, 21:58   #173
roger
 
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Oct 2006

22·5·13 Posts
Default COMPLETION

Here's the file: http://www.freedrive.com/file/584861,twins_0-10k.xlsx (hope the link works this time)

and list

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9555		1288809
9556		39051885
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9558		149770623
9559		9387285
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9562		16153257
9563		25854081
9564		13386357
9565		1197069
9566		108644745
9567		55116621
9568		5929545
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9570		9926655
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9605		75333951
9606		13396533
9607		46338255
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9609		7973049
9610		146510553
9611		111073479
9612		64784163
9613		41724615
9614		4355733
9615		8721309
9616		9161865
9617		100495455
9618		649233
9619		30730191
9620		52460577
9621		82886529
9622		72552633
9623		68522265
9624		145471917
9625		20134449
9626		1372857
9627		14390031
9628		63105135
9629		39695271
9630		24763293
9631		15995769
9632		59902347
9633		32408679
9634		38735613
9635		24966735
9636		24100065
9637		46368531
9638		9893475
9639		673311
9640		26760903
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9642		46881753
9643		54735975
9644		32462727
9645		12158865
9646		21356595
9647		139624989
9648		633033
9649		17019309
9650		83194665
9651		1244829
9652		2337663
9653		56339511
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9656		4093323
9657		8202705
9658		38845977
9659		20764281
9660		9734463
9661		36460305
9662		123091557
9663		28317069
9664		7072995
9665		3509499
9666		84077667
9667		35290011
9668		34144593
9669		30950169
9670		5549385
9671		32220555
9672		6852417
9673		19497855
9674		20980305
9675		1801485
9676		109912605
9677		89117049
9678		9901785
9679		39649611
9680		22897497
9681		19225395
9682		71762847
9683		9374781
9684		15434793
9685		30178839
9686		7740513
9687		83823885
9688		521775
9689		7770399
9690		7688037
9691		77329611
9692		84190203
9693		900231
9694		34183143
9695		22020201
9696		5340303
9697		17933355
9698		50882037
9699		5147775
9700		19580763
9701		20499171
9702		164243823
9703		76081455
9704		362457
9705		60085779
9706		3403503
9707		13372671
9708		4250727
9709		208362015
9710		119216187
9711		17649699
9712		28584285
9713		35324409
9714		5066145
9715		46998561
9716		26923977
9717		8752419
9718		36748497
9719		92467959
9720		20921637
9721		83249301
9722		76948467
9723		11972595
9724		44363205
9725		142920135
9726		10008243
9727		23513349
9728		32125257
9729		121080339
9730		55917657
9731		40087575
9732		17918355
9733		9329091
9734		10867227
9735		54939525
9736		16352307
9737		3049959
9738		140572383
9739		16514055
9740		9459807
9741		2699811
9742		37167327
9743		38725149
9744		55293765
9745		31815891
9746		5997603
9747		15980535
9748		41128173
9749		19421175
9750		158787543
9751		3297819
9752		27630537
9753		60441819
9754		1762353
9755		293475
9756		28820025
9757		6776001
9758		26379615
9759		2622855
9760		3551385
9761		43999761
9762		129460755
9763		37544355
9764		6052683
9765		51092619
9766		677235
9767		54987351
9768		40051485
9769		12067131
9770		29739717
9771		12005319
9772		32313387
9773		9502359
9774		132765747
9775		27414801
9776		25033803
9777		143832531
9778		1655253
9779		29252241
9780		13561245
9781		5507901
9782		12735633
9783		66199455
9784		2047533
9785		32354655
9786		9003705
9787		9944691
9788		80090283
9789		172982211
9790		3723273
9791		53511795
9792		3267273
9793		33947961
9794		25715283
9795		67333929
9796		57391635
9797		40524735
9798		21102345
9799		63475515
9800		47025597
9801		24427965
9802		41312985
9803		6162981
9804		10172685
9805		11163711
9806		15023667
9807		6389085
9808		14435757
9809		68134149
9810		64667067
9811		58207875
9812		39456477
9813		32369535
9814		15003015
9815		46314111
9816		19343163
9817		25143435
9818		21057225
9819		38505159
9820		20644827
9821		69099285
9822		70951797
9823		3949959
9824		13938303
9825		21565551
9826		14112243
9827		88983759
9828		47321283
9829		18000879
9830		4978707
9831		31071141
9832		4232943
9833		103442535
9834		33218325
9835		1755081
9836		5785737
9837		183196851
9838		111496947
9839		99114855
9840		38864193
9841		9821019
9842		5919375
9843		104536155
9844		117363
9845		5602311
9846		7734207
9847		104221599
9848		60186003
9849		28723929
9850		23838327
9851		36643599
9852		18007407
9853		2972349
9854		56477337
9855		66695709
9856		160469967
9857		2556525
9858		30864195
9859		31173885
9860		11541867
9861		62474289
9862		34856607
9863		19644009
9864		10052163
9865		87669819
9866		3489837
9867		59025675
9868		8532603
9869		33891
9870		10650273
9871		93785715
9872		11591013
9873		20354049
9874		25920663
9875		19665939
9876		59291643
9877		47076519
9878		129020823
9879		11104935
9880		30697287
9881		22924689
9882		3800583
9883		14549799
9884		48443997
9885		93014595
9886		168718293
9887		31405959
9888		50408907
9889		443961
9890		76510857
9891		20364615
9892		78118713
9893		14871825
9894		125393595
9895		17797725
9896		27545553
9897		17157441
9898		34869837
9899		50345901
9900		1538763
9901		77139831
9902		337137
9903		4508025
9904		3714417
9905		13789815
9906		136994475
9907		5878005
9908		8066325
9909		2479701
9910		41459763
9911		21333885
9912		80839425
9913		17644839
9914		21720567
9915		46843569
9916		20841303
9917		20661789
9918		41167737
9919		105651639
9920		38832825
9921		20859351
9922		45096357
9923		64778841
9924		66181353
9925		5648931
9926		5060157
9927		61895619
9928		127001895
9929		82610121
9930		92261277
9931		4439889
9932		33980055
9933		10109811
9934		82866993
9935		188381991
9936		57798387
9937		15941715
9938		73967655
9939		50674041
9940		32018043
9941		14024781
9942		140805
9943		38011521
9944		3534003
9945		11966871
9946		2565087
9947		48265461
9948		144404523
9949		36507375
9950		117980643
9951		10833459
9952		7274295
9953		1044189
9954		8630577
9955		18200919
9956		24357033
9957		16821075
9958		39798795
9959		117501219
9960		159312057
9961		84249165
9962		69378795
9963		68651109
9964		34915977
9965		37616229
9966		39764403
9967		22661379
9968		12328575
9969		6274635
9970		7755645
9971		57090561
9972		51452823
9973		24528015
9974		17098623
9975		302811
9976		5584677
9977		113292351
9978		8199735
9979		15732519
9980		38306517
9981		12665181
9982		33114723
9983		12378159
9984		5886513
9985		51790359
9986		119061393
9987		4808199
9988		32248263
9989		63204765
9990		65503377
9991		68865069
9992		16789905
9993		35536371
9994		48459945
9995		35371251
9996		31524777
9997		45018969
9998		92940765
9999		594501
10000		10642317
Doublechecking all k/n twin values now.

Last fiddled with by roger on 2008-11-30 at 22:19
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Old 2008-11-30, 22:50   #174
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Doublechecking complete: 10 errors out of 10000 n-values.

7944825*2^2692+1 is not prime. Proth RES64: C280A4BF19EB4EEF Time: 24.272 ms.
32325705*2^6424-1 is not prime. LLR Res64: FB885E049182D30A Time : 137.967 ms.
25376805*2^6663-1 is not prime. LLR Res64: FC5B8163B88A04A5 Time : 142.944 ms.
33840285*2^6664-1 is not prime. LLR Res64: 4A976AD7998E69C5 Time : 143.500 ms.
18157833*2^6807-1 is not prime. LLR Res64: D4AC79501000544A Time : 164.336 ms.
14938203*2^6828-1 is not prime. LLR Res64: 0CA5522D21650707 Time : 151.220 ms.
71835525*2^7000-1 is not prime. LLR Res64: 17D9F6A236E93FF8 Time : 170.266 ms.
10358415*2^7874-1 is not prime. LLR Res64: 08D4A1A5E5CBAFEE Time : 220.077 ms.
62159043*2^7896-1 is not prime. LLR Res64: BC9F736A88A8A996 Time : 223.435 ms.
36551361*2^8987-1 is not prime. LLR Res64: D6F9FC0DA6D6465E Time : 349.487 ms.

Will search for correct values.
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Old 2008-12-01, 06:54   #175
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Double-check corrections:

11387763*2^2692+-1
26854965*2^6663+-1
44337243*2^6664+-1
19109169*2^6807+-1
34382745*2^6828+-1
84561177*2^7000+-1
36068043*2^7874+-1
75170223*2^7896+-1

n=6424 and n=8987 are as yet unknown, I'll check those tomorrow.

Last fiddled with by roger on 2008-12-01 at 06:54
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Old 2008-12-02, 03:37   #176
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Corrections complete. File at http://www.freedrive.com/file/586345,twins_0-10k.xlsx.

Other twin areas searched:
Code:
n=	k= (millions)
33200	227.9
34528	56.5
34543	5
38183	7.37
40000	0.74
40001	5.75
40002	20
40003	10.68
40004	50
40011	5
40012	5
40013	5
45321	5
50000	1.17
50001	1
50002	1
50003	2
50004	1M<k<3
50005	8.95
55555	4.42
57557	5
59729	5
59747	13.1
59753	5
59771	5
61855	1
62627	30
63337	5
67777	5
70207	5
71899	5
72727	10
73237	5
74527	10
75000	100
75075	56.83
75937	10
76000	50
76067	2
76068	2
76069	2
76070	2
76071	2
76072	2
76073	1
76074	0.191
76075	3
76076	2
76077	2
76078	3
76079	2
76080	2
76081	2
76082	2
76083	2
76084	8.589
76085	2
76086	1.218
76087	3
76088	2
76089	2
76090	2
76091	2
76092	1
76093	2
76094	2
76095	2
76096	0.504
76097	0-2, 3-5
76098	2
76099	2
76100	2
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