List of most small twins of form k*2^n+/-1 - Page 18

roger · 2010-06-23, 03:53

I'm wondering also if there's a list of what ranges have been searched so as not to duplicate work.

Mine:

Code:

n	k (in millions)
15384	40
23087	150
27283	50
33200	227.9
34528	56.5
34543	5
36347	1
38183	7.37
38938	1
40000	0.74
40001	5.75
40002	20
40003	10.68
40004	50
40011	5
40012	5
40013	5
45321	5
47015	54.5
48023	168
50000	1.17
50001	1
50002	1
50003	2
50004	1M<k<3
50005	8.95
50363	0
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
83047	1.72

I've also sieving for 76101<n<76150 for k<1M.

roger · 2010-06-26, 10:06

56487159*2⁴⁷⁰¹⁵ is prime (14160 digits)

Have sieved 0<k<1M for 76101<n<76160 and varying ranges (mostly 1 or 2M) for 76067<n<76100.

currently testing n=83047 (at 4.6M)

n-value required to make the top-20 of Twin primes: 84049 (25299 digits)

We now have 292 twin primes with n-values above 10000; 102 of those have k-values below 100,000.

The average twin prime curve is now at k=0.8582*n^1.8172 (though of course this is now inaccurate due to the offset of lower k-values).

Oddball · 2010-09-17, 07:29

I just found my first 10,000+ digit twin:

32630865*2^33221-1 is prime! Time : 1.349 sec.
32630865*2^33221+1 is prime! Time: 1.359 sec.

That's also the lowest twin k for this n value.

roger · 2010-11-17, 06:36

Good news: 233145567*2⁷⁵⁰⁰⁰+-1 is prime :)

This result comes at 24.81% of the theoretical position for a n=75000 twin.
It's about 2100 digits short for the top-20 twin primes list, but I've got a few n's going that could make that list (eventually).

I'm going to doublecheck some of the (smaller) k-values from that list to see if they're the smallest and thus can be included on the chart.

Keep hunting!

roger · 2010-11-18, 05:48

Here's a (small) screenshot of the results plot:

http://www.flickr.com/photos/2822849...n/photostream/

(I'll see if I can get a higer-res copy up)

roger · 2010-11-28, 06:00

@whoever is maintaining the website:
a humble suggestion to change the chart type to have both axes logarithmic for a more easily-represented data set.

A few more small ones:

172214097*2³⁴⁵²⁸+-1
835335*2³⁹⁰¹⁴+-1

I also got a result (n=50364) using an even-k, so I'm doublechecking the lower k-values.

I'm hoping to get a 25000+ digit twin out there soon... who knows, maybe I'll get lucky with an n>100000 :) It's about time this project got a top-20 twin.

Here's the ranges I've had a look at so far:

Code:

n      k (millions)
15384	40
23087	150
27283	50
33200	363.488
34528	172.214
34543	5
36347	1
38183	7.37
38938	1
39014	0.835
40000	0.74
40001	5.75
40002	20
40003	10.68
40004	50
40011	5
40012	5
40013	5
42000	10
42001	10
42002	10
42003	10
42004	5
42005	5
42006	5
42007	5
42008	5
42009	5
42010	2.264
45058	5
45059	5
45060	5
45061	5
45062	5
45063	5
45064	5
45065	5
45066	4.738
45067	5
45068	10
45069	10
45070	10
45071	5
45072	4.324
45073	5
45074	5
45075	5
45321	5
47015	56.9
48023	168
50000	1.17
50001	1
50002	1
50003	2
50004	3
50005	8.95
50363	297.457
50364	0
53353	50
55056	5
55057	5
55058	5
55059	5
55060	5
55061	5
55062	5
55063	5
55064	5
55065	5
55066	5
55067	5
55068	5
55069	5
55070	5
55071	5
55555	4.42
57557	5
59729	5
59747	13.1
59753	5
59771	5
61855	1
62627	30
63337	5
65653	20
65657	1.835
67777	5
70207	5
70727	10
71899	5
72727	10
73237	5
74527	10
75000	233.146
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	5
76098	2
76099	2
76100	2
76101	1
76102	1
76103	1
76104	1
76105	1
76106	1
76107	1
76108	1
76109	1
76110	1
76111	1
76112	1
76113	1
76114	1
76115	1
76116	1
76117	1
76118	1
76119	1
76120	1
76121	1
76122	1
76123	1
76124	1
76125	1
76126	1
76127	1
76128	1
76129	1
76130	1
76131	1
76132	1
76133	1
76134	1
76135	1
76136	1
76137	1
76138	1
76139	1
76140	1
76141	1
76142	1
76143	1
76144	1
76145	1
76146	1
76147	1
76148	1
76149	1
76150	1
76151	1
76152	1
76153	1
76154	1
76155	1
76156	1
76157	1
76158	1
76159	1
76160	1
80000	1
80001	1
80002	1
80003	1
80004	1
80005	1
80006	1
80007	1
80008	1
80009	1
80010	1
83047	419.236
95147	1
98689	50
123456	10
123457	4.376
123458	10
123459	10
123460	10
123461	10
123462	10
123463	10
123464	10
123465	10
123466	10
123467	7.928
145235	7.929

EDIT: the percentage I mentioned for the n=75000 twin was in error - I was using an old trendline for the data; I updated it and applied a correction value based on previous datapoints of actual/theoretical twin value. The corrected value here was that 233145567*2⁷⁵⁰⁰⁰+-1 had a k-value approximately 12.5% usual.

kar_bon · 2010-11-28, 10:03

Quote:

Originally Posted by roger

@whoever is maintaining the website:
a humble suggestion to change the chart type to have both axes logarithmic for a more easily-represented data set.

If you mean this page I can do this the next days.

roger · 2010-11-29, 00:07

Yeah, that one :)

I've decided to resume searching the lower bounds here, noting that gdbarnes did k<1M for 10000<n<40000. Current range: 10100<n<10187.

Unfortunately I did also find an error in the data - n=8367 had the same k-value as n=8368 somehow; re-searching now.

kar_bon · 2010-11-29, 00:15

Quote:

Originally Posted by roger

Unfortunately I did also find an error in the data - n=8367 had the same k-value as n=8368 somehow; re-searching now.

My page contains for n=8367 the k-value 19939479 and for n=8368 k=17000355.

Or do you mean your data?

roger · 2010-11-29, 00:44

My data says 8368 = 17000355
and llr just came back with 8367 = 19939479
but I had 8366 as 19939479...

sorry, your data has the right value; I couldn't access the site earlier for some reason.

roger · 2010-11-29, 04:31

reserving 10100<n<11000

2010-06-26, 10:06	#189
roger Oct 2006 104₁₆ Posts	564871592⁴⁷⁰¹⁵ is prime (14160 digits) Have sieved 0<k<1M for 76101<n<76160 and varying ranges (mostly 1 or 2M) for 76067<n<76100. currently testing n=83047 (at 4.6M) n-value required to make the top-20 of Twin primes: 84049 (25299 digits) We now have 292 twin primes with n-values above 10000; 102 of those have k-values below 100,000. The average twin prime curve is now at k=0.8582n^1.8172 (though of course this is now inaccurate due to the offset of lower k-values). Last fiddled with by roger on 2010-06-26 at 10:07

2010-11-17, 06:36	#191
roger Oct 2006 104₁₆ Posts	Good news: 2331455672⁷⁵⁰⁰⁰+-1 is prime :) This result comes at 24.81% of the theoretical position for a n=75000 twin. It's about 2100 digits short for the top-20 twin primes list, but I've got a few n's going that could make that list (eventually). I'm going to doublecheck some of the (smaller) k-values from that list to see if they're the smallest and thus can be included on the chart. Keep hunting! Last fiddled with by roger on 2010-11-17 at 06:37*

2010-11-29, 00:07	#195
roger Oct 2006 2²×5×13 Posts	Yeah, that one :) I've decided to resume searching the lower bounds here, noting that gdbarnes did k<1M for 10000<n<40000. Current range: 10100<n<10187. Unfortunately I did also find an error in the data - n=8367 had the same k-value as n=8368 somehow; re-searching now. Last fiddled with by roger on 2010-11-29 at 01:00

2010-11-29, 00:44	#197
roger Oct 2006 104₁₆ Posts	My data says 8368 = 17000355 and llr just came back with 8367 = 19939479 but I had 8366 as 19939479... sorry, your data has the right value; I couldn't access the site earlier for some reason. Last fiddled with by roger on 2010-11-29 at 00:51

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2010-09-17, 07:29	#190
Oddball May 2010 499 Posts	I just found my first 10,000+ digit twin: 326308652^33221-1 is prime! Time : 1.349 sec. 326308652^33221+1 is prime! Time: 1.359 sec. That's also the lowest twin k for this n value.

2010-11-18, 05:48	#192
roger Oct 2006 260₁₀ Posts	Here's a (small) screenshot of the results plot: http://www.flickr.com/photos/2822849...n/photostream/ (I'll see if I can get a higer-res copy up)

2010-11-29, 04:31	#198
roger Oct 2006 2²·5·13 Posts	reserving 10100<n<11000