Difference between revisions of "Benchmarks of small admissible tuples"

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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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This is an obsolete page.
 
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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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|-
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!<math>k_0</math> !! 0 !! 1 !! 2 !! 3 !! 4 !! 5 !! 6 !! 7 !! 8 !! 9
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|-
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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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|-
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| 5500
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|-
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|-
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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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| -
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|-
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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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| -
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|-
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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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|-
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|-
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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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|-
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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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| -
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|-
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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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Latest revision as of 16:30, 20 June 2013

This is an obsolete page.