Finding optimal k0 values: Difference between revisions

Revision as of 09:47, 1 September 2013

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

**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{ k_0^{*} }[/math]	[math]\displaystyle{ k_0^{opt} }[/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]	Objective
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{ k_0^{*} }[/math]	[math]\displaystyle{ k_0^{opt} }[/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]	Objective
600/7	180/7	4	630	631	1.1639134E-02	9.1775130E-05	8.3989836E-03	193.9881059	3.02E-06	3.40E-08	1.00E-07	4.0614E-05

@@ Line 126: / Line 126: @@
 | 9.89E-08
 | -5.0940E-06
+|}
+{| {| 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.'''
+|-
+!colspan="3" | Instance
+!rowspan="2" | <math>k_0^{*}</math>
+!rowspan="2" | <math>k_0^{opt}</math>
+!colspan="4" | Parameters
+!colspan="3" | Error Terms
+!rowspan="2" | Objective
+|-
+!<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>
+|-
+|600/7
+| 180/7
+| 4
+| 630
+| [http://www.cs.cmu.edu/~xfxie/project/admissible/k0/sol_varpi600d7_631.mpl 631]
+| 1.1639134E-02
+| 9.1775130E-05
+| 8.3989836E-03
+| 193.9881059
+| 3.02E-06
+| 3.40E-08
+| 1.00E-07
+| 4.0614E-05
 |}