|
|
| (4 intermediate revisions by the same user not shown) |
| Line 1: |
Line 1: |
| Here is a table to fill in the best upper bounds available for small admissible tuples (1~5500) and a few of others.
| | This is an obsolete page. |
| | |
| | |
| == Rules ==
| |
| | |
| Efforts to fill in the blank fields in this table are very welcome. Here are the rules for the "Lucky Winner" game:
| |
| | |
| - "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.)
| |
| | |
| - "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).
| |
| | |
| Notes:
| |
| | |
| - 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.
| |
| | |
| == Records ==
| |
| | |
| {| border=1
| |
| |-
| |
| !<math>k_0</math> !! 0 !! 1 !! 2 !! 3 !! 4 !! 5 !! 6 !! 7 !! 8 !! 9
| |
| |-
| |
| | 6320
| |
| | -
| |
| | -
| |
| | -
| |
| | -
| |
| | -
| |
| | -
| |
| | -
| |
| | -
| |
| | -
| |
| | [http://www.cs.cmu.edu/~xfxie/project/admissible/admissible_6329_60726_14.txt '''60,726'''] (XFX-AVS)
| |
| |-
| |
| | 5500
| |
| | -
| |
| | -
| |
| | -
| |
| | -
| |
| | -
| |
| | -
| |
| | -
| |
| | -
| |
| | -
| |
| | -
| |
| |-
| |
| |-
| |
| |5450
| |
| | [http://www.cs.cmu.edu/~xfxie/project/admissible/admissible_5450_51498_-56176.txt 51,498] (XFX)
| |
| | [http://www.cs.cmu.edu/~xfxie/project/admissible/admissible_5451_51516_-55712.txt 51,516] (XFX)
| |
| | [http://math.mit.edu/~drew/admissible_5452_51520.txt '''51,520'''] (AVS)
| |
| | [http://math.mit.edu/~drew/admissible_5453_51526.txt '''51,526'''] (AVS)
| |
| | [http://www.cs.cmu.edu/~xfxie/project/admissible/admissible_5454_51534_-56228.txt 51,534] (XFX)
| |
| | [http://www.cs.cmu.edu/~xfxie/project/admissible/admissible_5455_51540_4678.txt '''51,540'''] (XFX&AVS)
| |
| | -
| |
| | -
| |
| | -
| |
| | -
| |
| | -
| |
| |-
| |
| |5440
| |
| | -
| |
| | -
| |
| | -
| |
| | -
| |
| | -
| |
| | -
| |
| | [http://www.cs.cmu.edu/~xfxie/project/admissible/admissible_5446_51456_2452.txt 51,456] (XFX)
| |
| | [http://www.cs.cmu.edu/~xfxie/project/admissible/admissible_5447_51462_-53908.txt 51,462] (XFX&AVS)
| |
| | [http://www.cs.cmu.edu/~xfxie/project/admissible/admissible_5448_51472_-53918.txt 51472] (XFX&AVS)
| |
| | -
| |
| |-
| |
| |4000
| |
| | [http://www.cs.cmu.edu/~xfxie/project/admissible/admissible_4000_36612_2554.txt 36,612] (XFX)
| |
| | -
| |
| | -
| |
| | -
| |
| | -
| |
| | -
| |
| | -
| |
| | -
| |
| | -
| |
| | -
| |
| |-
| |
| |-
| |
| |3000
| |
| | [http://www.cs.cmu.edu/~xfxie/project/admissible/admissible_3000_26606_-29486.txt 26,606] (XFX)
| |
| | -
| |
| | -
| |
| | -
| |
| | -
| |
| | -
| |
| | -
| |
| | -
| |
| | -
| |
| | -
| |
| |-
| |
| |2000
| |
| | [http://www.cs.cmu.edu/~xfxie/project/admissible/admissible_2000_16978_1108.txt 16,978] (TJE&XFX)
| |
| | -
| |
| | -
| |
| | -
| |
| | -
| |
| | -
| |
| | -
| |
| | -
| |
| | -
| |
| | -
| |
| |-
| |
| |1000
| |
| | [http://math.mit.edu/~drew/admissible_1000_7802.txt 7,802] (TJE&AVS)
| |
| | -
| |
| | -
| |
| | -
| |
| | -
| |
| | -
| |
| | -
| |
| | -
| |
| | -
| |
| | -
| |
| |-
| |
| |340
| |
| | -
| |
| | -
| |
| | [http://math.mit.edu/~drew/admissible_342_2328.txt 342] (TJE&AVS)
| |
| | -
| |
| | -
| |
| | -
| |
| | -
| |
| | -
| |
| | -
| |
| | -
| |
| |}
| |
| | |
| == Contributors ==
| |
| | |
| AVS: Andrew V. Sutherland
| |
| | |
| pedant
| |
| | |
| Scott Morrison
| |
| | |
| TJE: Thomas J. Engelsma
| |
| | |
| Wouter Castryck
| |
| | |
| XFX: xfxie
| |
| | |
| ZWS: Zhi-Wei Sun
| |
| | |
| '''[http://annals.math.princeton.edu/wp-content/uploads/YitangZhang.pdf Yitang Zhang]''': All work is based on Zhang's breakthrough paper.
| |
This is an obsolete page.
