Currently there may be errors shown on top of a page, because of a missing Wiki update (PHP version and extension DPL3).
Navigation
Topics Help • Register • News • History • How to • Sequences statistics • Template prototypes

Difference between revisions of "Riesel problem 3"

From Prime-Wiki
Jump to: navigation, search
(Interval 18 done)
(Level 19 finished with no additional primes)
 
(9 intermediate revisions by 3 users not shown)
Line 1: Line 1:
−
{{DISPLAYTITLE:The 3rd Riesel Problem}}
+
{{DISPLAYTITLE:Riesel problem 3, {{Kbn|-|k|2|n}}, {{Num|762701}} < {{Vk}} < {{Num|777149}}}}
−
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.
+
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}}
Line 11: Line 11:
 
| [[:Category:Riesel 2 3Intervals1|1]] || 2 || 3 || {{Num|6209}} || {{Num|{{PAGESINCATEGORY:Riesel 2 3Intervals1|pages|R}}}} || {{Num|1552}}
 
| [[:Category:Riesel 2 3Intervals1|1]] || 2 || 3 || {{Num|6209}} || {{Num|{{PAGESINCATEGORY:Riesel 2 3Intervals1|pages|R}}}} || {{Num|1552}}
 
|-
 
|-
−
| [[:Category:Riesel 2 3Intervals2|2]] || 4 || 7 || {{Num|4659}} || {{Num|{{PAGESINCATEGORY:Riesel 2 3Intervals2|pages|R}}}} || {{Num|1746}}
+
| [[:Category:Riesel 2 3Intervals2|2]] || 4 || 7 || {{Num|4657}} || {{Num|{{PAGESINCATEGORY:Riesel 2 3Intervals2|pages|R}}}} || {{Num|1746}}
 
|-
 
|-
 
| [[:Category:Riesel 2 3Intervals3|3]] || 8 || 15 || {{Num|2911}} || {{Num|{{PAGESINCATEGORY:Riesel 2 3Intervals3|pages|R}}}} || {{Num|1357}}
 
| [[:Category:Riesel 2 3Intervals3|3]] || 8 || 15 || {{Num|2911}} || {{Num|{{PAGESINCATEGORY:Riesel 2 3Intervals3|pages|R}}}} || {{Num|1357}}
Line 27: Line 27:
 
| [[: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
 
|-
 
|-
−
| [[:Category:Riesel 2 3Intervals10|10]] || {{Num|1024}} || {{Num|2047}} || 36 || {{Num|{{PAGESINCATEGORY:Riesel 2 3Intervals10|pages|R}}}} || 7
+
| [[:Category:Riesel 2 3Intervals10|10]] || {{Num|1024}} || {{Num|2047}} || 36 || class="color-Done" | 7 || 7
 
|-
 
|-
−
| [[:Category:Riesel 2 3Intervals11|11]] || {{Num|2048}} || {{Num|4095}} || 29 || {{Num|{{PAGESINCATEGORY:Riesel 2 3Intervals11|pages|R}}}} || 6
+
| [[:Category:Riesel 2 3Intervals11|11]] || {{Num|2048}} || {{Num|4095}} || 29 || class="color-Done" | 6 || 6
 
|-
 
|-
−
| [[:Category:Riesel 2 3Intervals12|12]] || {{Num|4096}} || {{Num|8191}} || 23 || {{Num|{{PAGESINCATEGORY:Riesel 2 3Intervals12|pages|R}}}} || 6
+
| [[:Category:Riesel 2 3Intervals12|12]] || {{Num|4096}} || {{Num|8191}} || 23 || class="color-Done" | 6 || 6
 
|-
 
|-
−
| [[:Category:Riesel 2 3Intervals13|13]] || {{Num|8192}} || {{Num|16383}} || 17 || {{Num|{{PAGESINCATEGORY:Riesel 2 3Intervals13|pages|R}}}} || 2
+
| [[:Category:Riesel 2 3Intervals13|13]] || {{Num|8192}} || {{Num|16383}} || 17 || class="color-Done" | 2 || 2
 
|-
 
|-
−
| [[:Category:Riesel 2 3Intervals14|14]] || {{Num|16384}} || {{Num|32767}} || 15 || {{Num|{{PAGESINCATEGORY:Riesel 2 3Intervals14|pages|R}}}} || 3
+
| [[:Category:Riesel 2 3Intervals14|14]] || {{Num|16384}} || {{Num|32767}} || 15 || class="color-Done" | 3 || 3
 
|-
 
|-
−
| [[:Category:Riesel 2 3Intervals15|15]] || {{Num|32768}} || {{Num|65535}} || 12 || {{Num|{{PAGESINCATEGORY:Riesel 2 3Intervals15|pages|R}}}} || 2
+
| [[:Category:Riesel 2 3Intervals15|15]] || {{Num|32768}} || {{Num|65535}} || 12 || class="color-Done" | 2 || 2
 
|-
 
|-
−
| [[:Category:Riesel 2 3Intervals16|16]] || {{Num|65536}} || {{Num|131071}} || 10 || {{Num|{{PAGESINCATEGORY:Riesel 2 3Intervals16|pages|R}}}} || 3
+
| [[: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 || {{Num|{{PAGESINCATEGORY:Riesel 2 3Intervals17|pages|R}}}} || 2
+
| [[:Category:Riesel 2 3Intervals17|17]] || {{Num|131072}} || {{Num|262143}} || 7 || class="color-Done" | 2 || 2
 
|-
 
|-
 
| [[: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
 
|-
 
|-
−
| [[:Category:Riesel 2 3Intervals19|19]] || {{Num|524288}} || {{Num|1048576}} || 5 || {{Num|{{PAGESINCATEGORY:Riesel 2 3Intervals19|R}}}} || &ge; {{PAGESINCATEGORY:Riesel 2 3Intervals19|pages|R}}
+
| [[:Category:Riesel 2 3Intervals19|19]] || {{Num|524288}} || {{Num|1048575}} || 5 || class="color-Done" | 1 || 1
 
|-
 
|-
−
| [[: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}}
+
| [[:Category:Riesel 2 3Intervals20|20]] || {{Num|1048576}} || {{Num|2097151}} || 4 || {{Num|{{PAGESINCATEGORY:Riesel 2 3Intervals20|R}}}} || &ge; {{PAGESINCATEGORY:Riesel 2 3Intervals20|pages|R}}
 +
|-
 +
| [[: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}}
 
|}
 
|}
  
−
'''The current {{Vn}}<sub>max</sub> = {{Num|{{Multi Reservation:20-NMax}}}} as of {{Multi Reservation:20-Date}}.'''
+
[[: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}}
−
[[Category:Conjectures]]
+
[[Category:Riesel prime conjectures|3]]
 
[[Category:Riesel 2 3Intervals| ]]
 
[[Category:Riesel 2 3Intervals| ]]
−
[[Category:Riesel problem 3rd| ]]
+
[[Category:Riesel problem 3| ]]

Latest revision as of 18:52, 30 April 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 1 ≥ 1
unknown 2,097,152 ∞ 3 0 3

Multi Reservation 20: The current nmax = 2,000,000 as of 2024-09-06.

Riesel primes
Retrieved from "https://www.rieselprime.de/z/index.php?title=Riesel_problem_3&oldid=31649"