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{{DISPLAYTITLE:The 2nd Riesel Problem}}
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{{DISPLAYTITLE:Riesel problem 2, {{Kbn|-|k|2|n}}, {{Num|509203}} < {{Vk}} < {{Num|762701}}}}
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The '''2nd Riesel problem''' involves determining the smallest [[Riesel numbers]] {{Kbn|k|2|n}} for 509203 &lt; {{Vk}} &lt; 762701, the first and second Riesel k-values without any possible primes.
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The '''2nd Riesel problem''' involves determining the smallest [[Riesel number]]s {{Kbn|k|2|n}} for 509203 &lt; {{Vk}} &lt; 762701, the first and second 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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!{{V|m}}!!{{Vn}}<sub>min</sub>!!{{Vn}}<sub>max</sub>!!remain!!current!!target
 
!{{V|m}}!!{{Vn}}<sub>min</sub>!!{{Vn}}<sub>max</sub>!!remain!!current!!target
 
|-
 
|-
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| [[:Category:Riesel prime 2nd f0|0]] || 1 || 1 || {{Num|126748}} || {{Num|{{PAGESINCATEGORY:Riesel prime 2nd f0|pages|R}}}} || {{Num|18050}}
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| [[:Category:Riesel 2 2Intervals0|0]] || 1 || 1 || {{Num|126748}} || {{Num|{{PAGESINCATEGORY:Riesel 2 2Intervals0|pages|R}}}} || {{Num|18050}}
 
|-
 
|-
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| [[:Category:Riesel prime 2nd f1|1]] || 2 || 3 || {{Num|108698}} || {{Num|{{PAGESINCATEGORY:Riesel prime 2nd f1|pages|R}}}} || {{Num|27596}}
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| [[:Category:Riesel 2 2Intervals1|1]] || 2 || 3 || {{Num|108698}} || {{Num|{{PAGESINCATEGORY:Riesel 2 2Intervals1|pages|R}}}} || {{Num|27596}}
 
|-
 
|-
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| [[:Category:Riesel prime 2nd f2|2]] || 4 || 7 || {{Num|81102}} || {{Num|{{PAGESINCATEGORY:Riesel prime 2nd f2|pages|R}}}} || {{Num|30503}}
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| [[:Category:Riesel 2 2Intervals2|2]] || 4 || 7 || {{Num|81102}} || {{Num|{{PAGESINCATEGORY:Riesel 2 2Intervals2|pages|R}}}} || {{Num|30503}}
 
|-
 
|-
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| [[:Category:Riesel prime 2nd f3|3]] || 8 || 15 || {{Num|50599}} || {{Num|{{PAGESINCATEGORY:Riesel prime 2nd f3|pages|R}}}} || {{Num|23785}}
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| [[:Category:Riesel 2 2Intervals3|3]] || 8 || 15 || {{Num|50599}} || {{Num|{{PAGESINCATEGORY:Riesel 2 2Intervals3|pages|R}}}} || {{Num|23785}}
 
|-
 
|-
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| [[:Category:Riesel prime 2nd f4|4]] || 16 || 31 || {{Num|26814}} || {{Num|{{PAGESINCATEGORY:Riesel prime 2nd f4|pages|R}}}} || {{Num|13631}}
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| [[:Category:Riesel 2 2Intervals4|4]] || 16 || 31 || {{Num|26814}} || {{Num|{{PAGESINCATEGORY:Riesel 2 2Intervals4|pages|R}}}} || {{Num|13631}}
 
|-
 
|-
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| [[:Category:Riesel prime 2nd f5|5]] || 32 || 63 || {{Num|13183}} || {{Num|{{PAGESINCATEGORY:Riesel prime 2nd f5|pages|R}}}} || {{Num|6613}}
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| [[:Category:Riesel 2 2Intervals5|5]] || 32 || 63 || {{Num|13183}} || {{Num|{{PAGESINCATEGORY:Riesel 2 2Intervals5|pages|R}}}} || {{Num|6613}}
 
|-
 
|-
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| [[:Category:Riesel prime 2nd f6|6]] || 64 || 127 || {{Num|6570}} || {{Num|{{PAGESINCATEGORY:Riesel prime 2nd f6|pages|R}}}} || {{Num|3108}}
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| [[:Category:Riesel 2 2Intervals6|6]] || 64 || 127 || {{Num|6570}} || {{Num|{{PAGESINCATEGORY:Riesel 2 2Intervals6|pages|R}}}} || {{Num|3108}}
 
|-
 
|-
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| [[:Category:Riesel prime 2nd f7|7]] || 128 || 255 || {{Num|3462}} || {{Num|{{PAGESINCATEGORY:Riesel prime 2nd f7|pages|R}}}} || {{Num|1485}}
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| [[:Category:Riesel 2 2Intervals7|7]] || 128 || 255 || {{Num|3462}} || {{Num|{{PAGESINCATEGORY:Riesel 2 2Intervals7|pages|R}}}} || {{Num|1485}}
 
|-
 
|-
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| [[:Category:Riesel prime 2nd f8|8]] || 256 || 511 || {{Num|1977}} || {{Num|{{PAGESINCATEGORY:Riesel prime 2nd f8|pages|R}}}} || 774
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| [[:Category:Riesel 2 2Intervals8|8]] || 256 || 511 || {{Num|1977}} || {{Num|{{PAGESINCATEGORY:Riesel 2 2Intervals8|pages|R}}}} || 774
 
|-
 
|-
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| [[:Category:Riesel prime 2nd f9|9]] || 512 || {{Num|1023}} || {{Num|1203}} || {{Num|{{PAGESINCATEGORY:Riesel prime 2nd f9|pages|R}}}} || 422
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| [[:Category:Riesel 2 2Intervals9|9]] || 512 || {{Num|1023}} || {{Num|1203}} || {{Num|{{PAGESINCATEGORY:Riesel 2 2Intervals9|pages|R}}}} || 422
 
|-
 
|-
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| [[:Category:Riesel prime 2nd f10|10]] || {{Num|1024}} || {{Num|2047}} || 781 || {{Num|{{PAGESINCATEGORY:Riesel prime 2nd f10|pages|R}}}} || 228
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| [[:Category:Riesel 2 2Intervals10|10]] || {{Num|1024}} || {{Num|2047}} || 781 || {{Num|{{PAGESINCATEGORY:Riesel 2 2Intervals10|pages|R}}}} || 228
 
|-
 
|-
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| [[:Category:Riesel prime 2nd f11|11]] || {{Num|2048}} || {{Num|4095}} || 553 || {{Num|{{PAGESINCATEGORY:Riesel prime 2nd f11|pages|R}}}} || 172
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| [[:Category:Riesel 2 2Intervals11|11]] || {{Num|2048}} || {{Num|4095}} || 553 || {{Num|{{PAGESINCATEGORY:Riesel 2 2Intervals11|pages|R}}}} || 172
 
|-
 
|-
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| [[:Category:Riesel prime 2nd f12|12]] || {{Num|4096}} || {{Num|8191}} || 381 || class="color-Done" | 110 || 110
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| [[:Category:Riesel 2 2Intervals12|12]] || {{Num|4096}} || {{Num|8191}} || 381 || class="color-Done" | 110 || 110
 
|-
 
|-
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| [[:Category:Riesel prime 2nd f13|13]] || {{Num|8192}} || {{Num|16383}} || 271 || class="color-Done" | 66 || 66
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| [[:Category:Riesel 2 2Intervals13|13]] || {{Num|8192}} || {{Num|16383}} || 271 || class="color-Done" | 66 || 66
 
|-
 
|-
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| [[:Category:Riesel prime 2nd f14|14]] || {{Num|16384}} || {{Num|32767}} || 205 || class="color-Done" | 68 || 68
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| [[:Category:Riesel 2 2Intervals14|14]] || {{Num|16384}} || {{Num|32767}} || 205 || class="color-Done" | 68 || 68
 
|-
 
|-
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| [[:Category:Riesel prime 2nd f15|15]] || {{Num|32768}} || {{Num|65535}} || 137 || class="color-Done" | 29 || 29
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| [[:Category:Riesel 2 2Intervals15|15]] || {{Num|32768}} || {{Num|65535}} || 137 || class="color-Done" | 29 || 29
 
|-
 
|-
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| [[:Category:Riesel prime 2nd f16|16]] || {{Num|65536}} || {{Num|131071}} || 108 || class="color-Done" | 26 || 26
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| [[:Category:Riesel 2 2Intervals16|16]] || {{Num|65536}} || {{Num|131071}} || 108 || class="color-Done" | 26 || 26
 
|-
 
|-
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| [[:Category:Riesel prime 2nd f17|17]] || {{Num|131072}} || {{Num|262143}} || 82 || class="color-Done" | 13 || 13
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| [[:Category:Riesel 2 2Intervals17|17]] || {{Num|131072}} || {{Num|262143}} || 82 || class="color-Done" | 13 || 13
 
|-
 
|-
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| [[:Category:Riesel prime 2nd f18|18]] || {{Num|262144}} || {{Num|524287}} || 69 || class="color-Done" | 16 || 16
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| [[:Category:Riesel 2 2Intervals18|18]] || {{Num|262144}} || {{Num|524287}} || 69 || class="color-Done" | 16 || 16
 
|-
 
|-
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| [[:Category:Riesel prime 2nd f19|19]] || {{Num|524288}} || {{Num|1048575}} || 53 || {{Num|{{PAGESINCATEGORY:Riesel prime 2nd f19|R}}}} || ?
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| [[:Category:Riesel 2 2Intervals19|19]] || {{Num|524288}} || {{Num|1048575}} || 53 || class="color-Done" | 11 || 11
 
|-
 
|-
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| [[:Category:Riesel prime 2nd f20|20]] || {{Num|1048576}} || &infin; || ? || {{Num|{{PAGESINCATEGORY:Riesel prime 2nd f20|R}}}} || ?
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| [[:Category:Riesel 2 2Intervals20|20]] || {{Num|1048576}} || {{Num|2097151}} || 42 || class="color-Done" | 8 || 8
 
|-
 
|-
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| [[:Category:2nd Riesel Problem|unknown]] || {{Num|{{Multi Reservation:21-NMax}}}} || &infin; || {{#expr:51-{{PAGESINCATEGORY:Riesel prime 2nd f20|pages|R}}}} || class="color-Done" | {{#expr:{{PAGESINCATEGORY:2nd Riesel Problem|pages|R}}-1}} || -
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| [[:Category:Riesel 2 2Intervals21|21]] || {{Num|2097152}} || {{Num|4194303}} || 34 || class="color-Done" | 6 || 6
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|-
 +
| [[:Category:Riesel 2 2Intervals22|22]] || {{Num|4194304}} || {{Num|8388607}} || 28 || {{Num|{{PAGESINCATEGORY:Riesel 2 2Intervals22|R}}}} || &ge; {{PAGESINCATEGORY:Riesel 2 2Intervals22|pages|R}}
 +
|-
 +
| [[:Category:Riesel 2 2Intervals23|23]] || {{Num|8388608}} || {{Num|16777215}} || &le; 22 || {{Num|{{PAGESINCATEGORY:Riesel 2 2Intervals23|R}}}} || &ge; {{PAGESINCATEGORY:Riesel 2 2Intervals23|pages|R}}
 +
|-
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| [[:Category:Riesel problem 2|unknown]] || {{Num|16777216}} || &infin; || {{#expr:{{PAGESINCATEGORY:Riesel problem 2|pages|R}}-2}} || class="color-Done" | 0 || {{#expr:{{PAGESINCATEGORY:Riesel problem 2|pages|R}}-2}}
 
|}
 
|}
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'''The current {{Vn}}<sub>max</sub> = {{Num|{{Multi Reservation:21-NMax}}}} as of {{Multi Reservation:21-Date}}.'''
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[[:Multi Reservation:21|Multi Reservation 21]]: '''The current {{Vn}}<sub>max</sub> = {{Num|{{Multi Reservation:21-NMax}}}} as of {{Multi Reservation:21-Date}}.'''
  
 
{{Navbox Riesel primes}}
 
{{Navbox Riesel primes}}
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[[Category:Math]]
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[[Category:Riesel prime conjectures|2]]
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[[Category:Riesel 2 2Intervals| ]]
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[[Category:Riesel problem 2| ]]

Latest revision as of 06:41, 29 March 2024

The 2nd Riesel problem involves determining the smallest Riesel numbers k•2n-1 for 509203 < k < 762701, the first and second Riesel k-values without any possible primes.

 
 : completely included in Prime-Wiki
m nmin nmax remain current target
0 1 1 126,748 17 18,050
1 2 3 108,698 26 27,596
2 4 7 81,102 36 30,503
3 8 15 50,599 45 23,785
4 16 31 26,814 17 13,631
5 32 63 13,183 2 6,613
6 64 127 6,570 1 3,108
7 128 255 3,462 0 1,485
8 256 511 1,977 0 774
9 512 1,023 1,203 1 422
10 1,024 2,047 781 0 228
11 2,048 4,095 553 0 172
12 4,096 8,191 381 110 110
13 8,192 16,383 271 66 66
14 16,384 32,767 205 68 68
15 32,768 65,535 137 29 29
16 65,536 131,071 108 26 26
17 131,072 262,143 82 13 13
18 262,144 524,287 69 16 16
19 524,288 1,048,575 53 11 11
20 1,048,576 2,097,151 42 8 8
21 2,097,152 4,194,303 34 6 6
22 4,194,304 8,388,607 28 6 ≥ 6
23 8,388,608 16,777,215 ≤ 22 0 ≥ 0
unknown 16,777,216 ∞ 22 0 22

Multi Reservation 21: The current nmax = 8,000,000 as of 2024-03-31.

Riesel primes
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