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
[/code]

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

56487159*2[sup]47015[/sup] 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).

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.

Good news: 233145567*2[SUP]75000[/SUP]+-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!

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

[url]http://www.flickr.com/photos/28228492@N05/5186028727/sizes/l/in/photostream/[/url]

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

@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*2[SUP]34528[/SUP]+-1
835335*2[SUP]39014[/SUP]+-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
[/CODE]

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*2[SUP]75000[/SUP]+-1 had a k-value approximately 12.5% usual.

[QUOTE=roger;239001]@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.
[/QUOTE]

If you mean [url=http://www.rieselprime.de/Related/FirstKTwin.htm]this page[/url] I can do this the next days.

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.

[QUOTE=roger;239092]Unfortunately I did also find an error in the data - n=8367 had the same k-value as n=8368 somehow; re-searching now.[/QUOTE]

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

Or do you mean your data?

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.

reserving 10100<n<11000