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| Here is a table to fill in the best upper bounds available for small admissible tuples (1~10000).
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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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| == 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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| |5540
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| | [http://math.mit.edu/~drew/admissible_5453_51526.txt '''51,526'''] (AVS)
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| |5000
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| | [http://www.cs.cmu.edu/~xfxie/project/admissible/admissible_5000_46810_3946.txt 46,810] (XFX)
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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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| |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 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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Latest revision as of 16:30, 20 June 2013
This is an obsolete page.
