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(Fixing typo; streamlining interval 17)
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{{DISPLAYTITLE:The 3rd Riesel Problem}}
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{{DISPLAYTITLE:Riesel problem 3, {{Kbn|-|k|2|n}}, {{Num|762701}} < {{Vk}} < {{Num|777149}}}}
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The '''3rd Riesel problem''' involves determining the smallest [[Riesel number]]s {{Kbn|k|2|n}} for 762701 &lt; {{Vk}} &lt; 777149, the second and third Riesel {{Vk}}-values without any possible primes.
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The '''3rd Riesel problem''' involves determining the smallest [[Riesel number]]s {{Kbn|k|2|n}} for {{Num|762701}} &lt; {{Vk}} &lt; {{Num|777149}}, the second and third Riesel {{Vk}}-values without any possible primes.
  
 
:<div class="color-Done" style="width:4em; display:inline-block;">&nbsp;</div> : completely included in {{SITENAME}}
 
:<div class="color-Done" style="width:4em; display:inline-block;">&nbsp;</div> : completely included in {{SITENAME}}
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| [[:Category:Riesel 2 3Intervals9|9]] || 512 || {{Num|1023}} || 65 || {{Num|{{PAGESINCATEGORY:Riesel 2 3Intervals9|pages|R}}}} || 29
 
| [[:Category:Riesel 2 3Intervals9|9]] || 512 || {{Num|1023}} || 65 || {{Num|{{PAGESINCATEGORY:Riesel 2 3Intervals9|pages|R}}}} || 29
 
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|-
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| [[:Category:Riesel 2 3Intervals10|10]] || {{Num|1024}} || {{Num|2047}} || 36 || {{Num|{{PAGESINCATEGORY:Riesel 2 3Intervals10|pages|R}}}} || 7
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| [[:Category:Riesel 2 3Intervals10|10]] || {{Num|1024}} || {{Num|2047}} || 36 || class="color-Done" | 7 || 7
 
|-
 
|-
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| [[:Category:Riesel 2 3Intervals11|11]] || {{Num|2048}} || {{Num|4095}} || 29 || {{Num|{{PAGESINCATEGORY:Riesel 2 3Intervals11|pages|R}}}} || 6
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| [[:Category:Riesel 2 3Intervals11|11]] || {{Num|2048}} || {{Num|4095}} || 29 || class="color-Done" | 6 || 6
 
|-
 
|-
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| [[:Category:Riesel 2 3Intervals12|12]] || {{Num|4096}} || {{Num|8191}} || 23 || {{Num|{{PAGESINCATEGORY:Riesel 2 3Intervals12|pages|R}}}} || 6
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| [[:Category:Riesel 2 3Intervals12|12]] || {{Num|4096}} || {{Num|8191}} || 23 || class="color-Done" | 6 || 6
 
|-
 
|-
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| [[:Category:Riesel 2 3Intervals13|13]] || {{Num|8192}} || {{Num|16383}} || 17 || {{Num|{{PAGESINCATEGORY:Riesel 2 3Intervals13|pages|R}}}} || 2
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| [[:Category:Riesel 2 3Intervals13|13]] || {{Num|8192}} || {{Num|16383}} || 17 || class="color-Done" | 2 || 2
 
|-
 
|-
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| [[:Category:Riesel 2 3Intervals14|14]] || {{Num|16384}} || {{Num|32767}} || 15 || {{Num|{{PAGESINCATEGORY:Riesel 2 3Intervals14|pages|R}}}} || 3
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| [[:Category:Riesel 2 3Intervals14|14]] || {{Num|16384}} || {{Num|32767}} || 15 || class="color-Done" | 3 || 3
 
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|-
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| [[:Category:Riesel 2 3Intervals15|15]] || {{Num|32768}} || {{Num|65535}} || 12 || {{Num|{{PAGESINCATEGORY:Riesel 2 3Intervals15|pages|R}}}} || 2
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| [[:Category:Riesel 2 3Intervals15|15]] || {{Num|32768}} || {{Num|65535}} || 12 || class="color-Done" | 2 || 2
 
|-
 
|-
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| [[:Category:Riesel 2 3Intervals16|16]] || {{Num|65536}} || {{Num|131071}} || 10 || {{Num|{{PAGESINCATEGORY:Riesel 2 3Intervals16|pages|R}}}} || 3
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| [[:Category:Riesel 2 3Intervals16|16]] || {{Num|65536}} || {{Num|131071}} || 10 || class="color-Done" | 3 || 3
 
|-
 
|-
 
| [[:Category:Riesel 2 3Intervals17|17]] || {{Num|131072}} || {{Num|262143}} || 7 || class="color-Done" | 2 || 2
 
| [[:Category:Riesel 2 3Intervals17|17]] || {{Num|131072}} || {{Num|262143}} || 7 || class="color-Done" | 2 || 2
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| [[:Category:Riesel 2 3Intervals18|18]] || {{Num|262144}} || {{Num|524287}} || 5 || class="color-Done" | 0 || 0
 
| [[:Category:Riesel 2 3Intervals18|18]] || {{Num|262144}} || {{Num|524287}} || 5 || class="color-Done" | 0 || 0
 
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|-
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| [[:Category:Riesel 2 3Intervals19|19]] || {{Num|524288}} || {{Num|1048576}} || 5 || {{Num|{{PAGESINCATEGORY:Riesel 2 3Intervals19|R}}}} || &ge; {{PAGESINCATEGORY:Riesel 2 3Intervals19|pages|R}}
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| [[:Category:Riesel 2 3Intervals19|19]] || {{Num|524288}} || {{Num|1048575}} || 5 || {{Num|{{PAGESINCATEGORY:Riesel 2 3Intervals19|R}}}} || &ge; {{PAGESINCATEGORY:Riesel 2 3Intervals19|pages|R}}
 
|-
 
|-
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| [[:Category:Riesel problem 3rd|unknown]] || {{Num|524288}} || &infin; || {{#expr:{{PAGESINCATEGORY:Riesel problem 3rd|pages|R}}-1}} || class="color-Done" | 0 || {{#expr:{{PAGESINCATEGORY:Riesel problem 3rd|pages|R}}-1}}
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| [[:Category:Riesel 2 3Intervals20|20]] || {{Num|1048576}} || {{Num|2097151}} || &le; 4 || {{Num|{{PAGESINCATEGORY:Riesel 2 3Intervals20|R}}}} || &ge; {{PAGESINCATEGORY:Riesel 2 3Intervals20|pages|R}}
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|-
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| [[:Category:Riesel problem 3|unknown]] || {{Num|2097152}} || &infin; || {{#expr:{{PAGESINCATEGORY:Riesel problem 3|pages|R}}-1}} || class="color-Done" | 0 || {{#expr:{{PAGESINCATEGORY:Riesel problem 3|pages|R}}-1}}
 
|}
 
|}
  
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'''The current {{Vn}}<sub>max</sub> = {{Num|{{Multi Reservation:20-NMax}}}} as of {{Multi Reservation:20-Date}}.'''
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[[:Multi Reservation:20|Multi Reservation 20]]: '''The current {{Vn}}<sub>max</sub> = {{Num|{{Multi Reservation:20-NMax}}}} as of {{Multi Reservation:20-Date}}.'''
  
 
{{Navbox Riesel primes}}
 
{{Navbox Riesel primes}}
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[[Category:Conjectures]]
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[[Category:Riesel prime conjectures|3]]
 
[[Category:Riesel 2 3Intervals| ]]
 
[[Category:Riesel 2 3Intervals| ]]
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[[Category:Riesel problem 3rd| ]]
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[[Category:Riesel problem 3| ]]

Revision as of 04:47, 31 March 2024

The 3rd Riesel problem involves determining the smallest Riesel numbers k•2n-1 for 762,701 < k < 777,149, the second and third Riesel k-values without any possible primes.

 
 : completely included in Prime-Wiki
m nmin nmax remain current target
0 1 1 7,223 0 1,014
1 2 3 6,209 4 1,552
2 4 7 4,657 2 1,746
3 8 15 2,911 4 1,357
4 16 31 1,554 2 803
5 32 63 751 0 380
6 64 127 371 0 168
7 128 255 203 0 88
8 256 511 115 0 50
9 512 1,023 65 2 29
10 1,024 2,047 36 7 7
11 2,048 4,095 29 6 6
12 4,096 8,191 23 6 6
13 8,192 16,383 17 2 2
14 16,384 32,767 15 3 3
15 32,768 65,535 12 2 2
16 65,536 131,071 10 3 3
17 131,072 262,143 7 2 2
18 262,144 524,287 5 0 0
19 524,288 1,048,575 5 1 ≥ 1
20 1,048,576 2,097,151 ≤ 4 0 ≥ 0
unknown 2,097,152 ∞ 4 0 4

Multi Reservation 20: The current nmax = 1,100,000 as of 2024-04-30.

Riesel primes
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