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| Here is a table to fill in the best upper bounds available for small admissible tuples (1~5500) and a few of others.
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| == Rules ==
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| Efforts to fill in the blank fields in this table are very welcome. Here are the rules for the "Lucky Winner" game:
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| - "Winner" for each cell: You might enter each cell with a new tuple with the best upper bound and the abbreviation of your name (Your might append others' if your solution is obtained using others' work. It is encouraged to have a long chain to show the collaborative work.)
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| - "Lucky": Your cell will be "bold" if it is picked by an angel, if you are sufficiently lucky. The result will be qualified for showing in the [http://michaelnielsen.org/polymath1/index.php?title=Bounded_gaps_between_primes main page]. Your cell might be stroked through if the luck is not sustained (i.e., if the k0 claim is retracted).
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| Notes:
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| - Thomas J Engelsma have calculated upper bounds exactly for k0 up to 342, but he did not provide his tuples. So your contribution will be shown as TJE&<Your Name>, if your provide an optimal tuple.
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| - Update: Thomas J Engelsma has put his [http://www.opertech.com/primes/webdata data] online (for k0 in [2, 4507]), so there is no chance to claim optimal results for k0 up to 342 any more.
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| == Records ==
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| {| border=1
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| !<math>k_0</math> !! 0 !! 1 !! 2 !! 3 !! 4 !! 5 !! 6 !! 7 !! 8 !! 9
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| | 6320
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| | [http://www.cs.cmu.edu/~xfxie/project/admissible/admissible_6329_60726_14.txt '''60,726'''] (XFX-AVS)
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| | 5500
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| |5450
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| | [http://www.cs.cmu.edu/~xfxie/project/admissible/admissible_5450_51498_-56176.txt 51,498] (XFX)
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| | [http://www.cs.cmu.edu/~xfxie/project/admissible/admissible_5451_51516_-55712.txt 51,516] (XFX)
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| | [http://math.mit.edu/~drew/admissible_5452_51520.txt '''51,520'''] (AVS)
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| | [http://math.mit.edu/~drew/admissible_5453_51526.txt '''51,526'''] (AVS)
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| | [http://www.cs.cmu.edu/~xfxie/project/admissible/admissible_5454_51534_-56228.txt 51,534] (XFX)
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| | [http://www.cs.cmu.edu/~xfxie/project/admissible/admissible_5455_51540_4678.txt '''51,540'''] (XFX&AVS)
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| |5440
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| | [http://www.cs.cmu.edu/~xfxie/project/admissible/admissible_5446_51456_2452.txt 51,456] (XFX)
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| | [http://www.cs.cmu.edu/~xfxie/project/admissible/admissible_5447_51462_-53908.txt 51,462] (XFX&AVS)
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| | [http://www.cs.cmu.edu/~xfxie/project/admissible/admissible_5448_51472_-53918.txt 51472] (XFX&AVS)
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| |4000
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| | [http://www.cs.cmu.edu/~xfxie/project/admissible/admissible_4000_36612_2554.txt 36,612] (XFX)
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| |3000
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| | [http://www.cs.cmu.edu/~xfxie/project/admissible/admissible_3000_26606_-29486.txt 26,606] (XFX)
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| |2000
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| | [http://www.cs.cmu.edu/~xfxie/project/admissible/admissible_2000_16978_1108.txt 16,978] (TJE&XFX)
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| |1000
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| | [http://math.mit.edu/~drew/admissible_1000_7802.txt 7,802] (TJE&AVS)
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| |340
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| | [http://math.mit.edu/~drew/admissible_342_2328.txt 342] (TJE&AVS)
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| |}
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| == Contributors ==
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| AVS: Andrew V. Sutherland
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| pedant
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| Scott Morrison
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| TJE: Thomas J. Engelsma
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| Wouter Castryck
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| XFX: xfxie
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| ZWS: Zhi-Wei Sun
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| '''[http://annals.math.princeton.edu/wp-content/uploads/YitangZhang.pdf Yitang Zhang]''': All work is based on Zhang's breakthrough paper.
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This is an obsolete page.
