Finding optimal k0 values: Difference between revisions

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→‎Benchmarks: Failure table
Line 139: Line 139:
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|-
!<math>c_{\varpi}</math> !! <math>~c_{\delta}~</math> !! <math>~i~</math> !! <math>\varpi</math> !! <math>~\delta~</math> !! <math>~\delta'~</math> !! <math>~A~</math> !! <math>~\kappa_1~</math> !! <math>~\kappa_2~</math> !! <math>~\kappa_3~</math>
!<math>c_{\varpi}</math> !! <math>~c_{\delta}~</math> !! <math>~i~</math> !! <math>\varpi</math> !! <math>~\delta~</math> !! <math>~\delta'~</math> !! <math>~A~</math> !! <math>~\kappa_1~</math> !! <math>~\kappa_2~</math> !! <math>~\kappa_3~</math>
|-
| 348
| 68
| 1
| 5446
| [http://www.cs.cmu.edu/~xfxie/project/admissible/k0/sol_varpi348_5446.mpl 5446]
| 1.1666317E-02
| 1.1659847E-06
| 1.4881806E-03
| 2558.927043
| 6.15E-09
| 1.81E-12
| 1.34E-10
| 1.7560E-07
|-
| 168
| 48
| 2
| 1781
| [http://www.cs.cmu.edu/~xfxie/project/admissible/k0/sol_varpi168_1782.mpl 1782]
| 1.1663695E-02
| 9.9043741E-06
| 3.7130742E-03
| 757.367314
| 1.59E-07
| 3.26E-10
| 3.21E-09
| 2.5064E-06
|-
| 148
| 33
| 1
| 1465
| [http://www.cs.cmu.edu/~xfxie/project/admissible/k0/sol_varpi148_1465.mpl 1465]
| 1.1663259E-02
| 1.1359571E-05
| 4.7002144E-03
| 625.147981
| 9.16E-08
| 9.27E-11
| 3.28E-09
| 9.3639E-06
|-
|140
| 32
| 1
| 1345
| [http://www.cs.cmu.edu/~xfxie/project/admissible/k0/sol_varpi140_1345.mpl 1345]
| 1.1662709E-02
| 1.3191723E-05
| 5.0558681E-03
| 568.169087
| 1.11E-07
| 1.23E-10
| 4.94E-10
| 6.6030E-06
|-
|116
| 30
| 1
| 1006
| [http://www.cs.cmu.edu/~xfxie/project/admissible/k0/sol_varpi116_1006.mpl 1006]
| 1.1660089E-02
| 2.1925014E-05
| 6.4287825E-03
| 408.551108
| 2.33E-07
| 3.89E-10
| 1.24E-08
| 1.5183E-05
|-
|-
|108
| 30
| 1
| 901
| [http://www.cs.cmu.edu/~xfxie/project/admissible/k0/sol_varpi108_901.mpl 901]
| 1.1658682E-02
| 2.6615167E-05
| 7.0404135E-03
| 359.584585
| 3.08E-07
| 5.97E-10
| 1.68E-08
| 1.4703E-05
|-
|280/3
| 80/3
| 2
| 719
| [http://www.cs.cmu.edu/~xfxie/project/admissible/k0/sol_varpi280d3_719.mpl 719]
| 1.1651479E-02
| 5.0626919E-05
| 8.0520479E-03
| 259.837059
| 1.04E-06
| 4.96E-09
| 4.46E-08
| 3.1365E-05
|-
|-
|600/7
|600/7
Line 148: Line 247:
| 9.1775130E-05
| 9.1775130E-05
| 8.3989836E-03
| 8.3989836E-03
| 193.9881059
| 193.988106
| 3.02E-06
| 3.02E-06
| 3.40E-08
| 3.40E-08

Revision as of 11:40, 1 September 2013

This is a sub-page for the Polymath8 project "bounded gaps between primes".

Benchmarks

Optimal results at [math]\displaystyle{ k_0^{opt} }[/math] for some instances of [math]\displaystyle{ c_\varpi, c_\delta, i }[/math] values.
Instance [math]\displaystyle{ k_0^{*} }[/math] [math]\displaystyle{ k_0^{opt} }[/math] Parameters Error Terms Objective
[math]\displaystyle{ c_{\varpi} }[/math] [math]\displaystyle{ ~c_{\delta}~ }[/math] [math]\displaystyle{ ~i~ }[/math] [math]\displaystyle{ \varpi }[/math] [math]\displaystyle{ ~\delta~ }[/math] [math]\displaystyle{ ~\delta'~ }[/math] [math]\displaystyle{ ~A~ }[/math] [math]\displaystyle{ ~\kappa_1~ }[/math] [math]\displaystyle{ ~\kappa_2~ }[/math] [math]\displaystyle{ ~\kappa_3~ }[/math]
348 68 1 5446 5447 2.8733352E-03 1.1670730E-06 1.4955362E-03 2559.258877 5.63E-09 1.52E-12 8.54E-11 -1.1881E-06
168 48 2 1781 1783 5.9495534E-03 9.8965035E-06 3.7117059E-03 757.8242621 1.58E-07 3.24E-10 3.65E-09 -5.9684E-06
148 33 1 1465 1466 6.7542244E-03 1.1357314E-05 4.7101572E-03 626.6135921 8.79E-08 8.57E-11 3.63E-09 -2.2867E-06
140 32 1 1345 1346 7.1398444E-03 1.3180858E-05 5.0540952E-03 577.7849932 1.10E-07 1.22E-10 4.75E-09 -6.7812E-06
116 30 1 1006 1007 8.6150249E-03 2.1903801E-05 6.4285376E-03 408.9674914 2.30E-07 3.80E-10 1.17E-08 -6.2560E-06
108 30 1 901 902 9.2518776E-03 2.6573843E-05 7.0318847E-03 359.6376563 3.08E-07 6.00E-10 1.76E-08 -1.0924E-05
280/3 80/3 2 719 720 1.0699851E-02 5.0521044E-05 8.0398983E-03 260.2624368 1.04E-06 4.98E-09 4.33E-08 -5.5687E-06
600/7 180/7 4 630 632 1.1639206E-02 9.1536798E-05 8.3866560E-03 194.5246551 3.01E-06 3.40E-08 9.89E-08 -5.0940E-06
"Failure" results at [math]\displaystyle{ (k_0^{opt}-1) }[/math] for some instances of [math]\displaystyle{ c_\varpi, c_\delta, i }[/math] values.
Instance [math]\displaystyle{ k_0^{*} }[/math] [math]\displaystyle{ k_0^{opt} }[/math] Parameters Error Terms Objective
[math]\displaystyle{ c_{\varpi} }[/math] [math]\displaystyle{ ~c_{\delta}~ }[/math] [math]\displaystyle{ ~i~ }[/math] [math]\displaystyle{ \varpi }[/math] [math]\displaystyle{ ~\delta~ }[/math] [math]\displaystyle{ ~\delta'~ }[/math] [math]\displaystyle{ ~A~ }[/math] [math]\displaystyle{ ~\kappa_1~ }[/math] [math]\displaystyle{ ~\kappa_2~ }[/math] [math]\displaystyle{ ~\kappa_3~ }[/math]
348 68 1 5446 5446 1.1666317E-02 1.1659847E-06 1.4881806E-03 2558.927043 6.15E-09 1.81E-12 1.34E-10 1.7560E-07
168 48 2 1781 1782 1.1663695E-02 9.9043741E-06 3.7130742E-03 757.367314 1.59E-07 3.26E-10 3.21E-09 2.5064E-06
148 33 1 1465 1465 1.1663259E-02 1.1359571E-05 4.7002144E-03 625.147981 9.16E-08 9.27E-11 3.28E-09 9.3639E-06
140 32 1 1345 1345 1.1662709E-02 1.3191723E-05 5.0558681E-03 568.169087 1.11E-07 1.23E-10 4.94E-10 6.6030E-06
116 30 1 1006 1006 1.1660089E-02 2.1925014E-05 6.4287825E-03 408.551108 2.33E-07 3.89E-10 1.24E-08 1.5183E-05
108 30 1 901 901 1.1658682E-02 2.6615167E-05 7.0404135E-03 359.584585 3.08E-07 5.97E-10 1.68E-08 1.4703E-05
280/3 80/3 2 719 719 1.1651479E-02 5.0626919E-05 8.0520479E-03 259.837059 1.04E-06 4.96E-09 4.46E-08 3.1365E-05
600/7 180/7 4 630 631 1.1639134E-02 9.1775130E-05 8.3989836E-03 193.988106 3.02E-06 3.40E-08 1.00E-07 4.0614E-05
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