Finding optimal k0 values: Difference between revisions
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== Benchmarks == | == Benchmarks == | ||
{| {| class="wikitable" border=1 style="margin: 1em auto 1em auto;" | {| {| class="wikitable" border=1 style="margin: 1em auto 1em auto;" | ||
|+ '''Optimal results at <math>k_0^{opt}</math> for some instances of <math>c_\varpi, c_\delta, i</math> values.''' | |+ '''Optimal results at <math>k_0 = k_0^{opt}</math> for some instances of <math>c_\varpi, c_\delta, i</math> values.''' | ||
|- | |- | ||
!colspan="3" | Instance | !colspan="3" | Instance | ||
!rowspan="2" | <math>k_0^{*}</math> | !rowspan="2" | <math>k_0^{*}</math> | ||
!rowspan="2" | <math>k_0 | !rowspan="2" | <math>k_0</math> | ||
!colspan="4" | Parameters | !colspan="4" | Parameters | ||
!colspan="3" | Error Terms | !colspan="3" | Error Terms | ||
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{| {| class="wikitable" border=1 style="margin: 1em auto 1em auto;" | {| {| class="wikitable" border=1 style="margin: 1em auto 1em auto;" | ||
|+ '''"Failure" results at <math>(k_0^{opt}-1)</math> for some instances of <math>c_\varpi, c_\delta, i</math> values.''' | |+ '''"Failure" results at <math>k_0=(k_0^{opt}-1)</math> for some instances of <math>c_\varpi, c_\delta, i</math> values.''' | ||
|- | |- | ||
!colspan="3" | Instance | !colspan="3" | Instance | ||
!rowspan="2" | <math>k_0^{*}</math> | !rowspan="2" | <math>k_0^{*}</math> | ||
!rowspan="2" | <math>k_0 | !rowspan="2" | <math>k_0</math> | ||
!colspan="4" | Parameters | !colspan="4" | Parameters | ||
!colspan="3" | Error Terms | !colspan="3" | Error Terms | ||
Revision as of 11:42, 1 September 2013
This is a sub-page for the Polymath8 project "bounded gaps between primes".
Benchmarks
| Instance | [math]\displaystyle{ k_0^{*} }[/math] | [math]\displaystyle{ k_0 }[/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 |
| Instance | [math]\displaystyle{ k_0^{*} }[/math] | [math]\displaystyle{ k_0 }[/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 |
