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Difference between revisions of "Riesel problem 2"

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The '''2nd Riesel problem''' involves determining the smallest [[Riesel numbers]] {{Kbn|k|2|n}} for 509203 < {{Vk}} < 762701, the first and second Riesel k-values without any possible primes.
 
The '''2nd Riesel problem''' involves determining the smallest [[Riesel numbers]] {{Kbn|k|2|n}} for 509203 < {{Vk}} < 762701, the first and second Riesel k-values without any possible primes.
  
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:<div style="width:4em; background:PaleGreen; display:inline-block;">&nbsp;</div> : completely included in {{SITENAME}}
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:<div class="color-Done" style="width:4em; display:inline-block;">&nbsp;</div> : completely included in {{SITENAME}}
  
 
{| class="wikitable" style="text-align:right;"
 
{| class="wikitable" style="text-align:right;"
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| [[:Category:Riesel prime 2nd f11|11]] || {{Num|2048}} || {{Num|4095}} || 553 || {{Num|{{PAGESINCATEGORY:Riesel prime 2nd f11|pages|R}}}} || 172
 
| [[: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 prime 2nd f12|12]] || {{Num|4096}} || {{Num|8191}} || 381 || style="background:PaleGreen;" | 110 || 110
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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 prime 2nd f13|13]] || {{Num|8192}} || {{Num|16383}} || 271 || style="background:PaleGreen;" | 66 || 66
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| [[:Category:Riesel prime 2nd f13|13]] || {{Num|8192}} || {{Num|16383}} || 271 || class="color-Done" | 66 || 66
 
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|-
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| [[:Category:Riesel prime 2nd f14|14]] || {{Num|16384}} || {{Num|32767}} || 205 || style="background:PaleGreen;" | 68 || 68
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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 prime 2nd f15|15]] || {{Num|32768}} || {{Num|65535}} || 137 || style="background:PaleGreen;" | 29 || 29
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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 prime 2nd f16|16]] || {{Num|65536}} || {{Num|131071}} || 108 || style="background:PaleGreen;" | 26 || 26
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| [[:Category:Riesel prime 2nd f16|16]] || {{Num|65536}} || {{Num|131071}} || 108 || class="color-Done" | 26 || 26
 
|-
 
|-
 
| [[:Category:Riesel prime 2nd f17|17]] || {{Num|131072}} || {{Num|262143}} || 82 || style="background:PaleGreen;" | 13 || 13
 
| [[:Category:Riesel prime 2nd f17|17]] || {{Num|131072}} || {{Num|262143}} || 82 || style="background:PaleGreen;" | 13 || 13
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| [[:Category:Riesel prime 2nd f20|20]] || {{Num|1048576}} || &infin; || ? || {{Num|{{PAGESINCATEGORY:Riesel prime 2nd f20|R}}}} || ?
 
| [[:Category:Riesel prime 2nd f20|20]] || {{Num|1048576}} || &infin; || ? || {{Num|{{PAGESINCATEGORY:Riesel prime 2nd f20|R}}}} || ?
 
|-
 
|-
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| [[:Category:2nd Riesel Problem|unknown]] || {{Num|{{Multi Reservation:21-NMax}}}} || &infin; || {{#expr:62-{{PAGESINCATEGORY:Riesel prime 2nd f20|pages|R}}}} || style="background:PaleGreen;" | {{#expr:{{PAGESINCATEGORY:2nd Riesel Problem|pages|R}}-1}} || -
+
| [[:Category:2nd Riesel Problem|unknown]] || {{Num|{{Multi Reservation:21-NMax}}}} || &infin; || {{#expr:62-{{PAGESINCATEGORY:Riesel prime 2nd f20|pages|R}}}} || class="color-Done" | {{#expr:{{PAGESINCATEGORY:2nd Riesel Problem|pages|R}}-1}} || -
 
|}
 
|}
 
'''The current {{Vn}}<sub>max</sub> = {{Num|{{Multi Reservation:21-NMax}}}} as of {{Multi Reservation:21-Date}}.'''
 
'''The current {{Vn}}<sub>max</sub> = {{Num|{{Multi Reservation:21-NMax}}}} as of {{Multi Reservation:21-Date}}.'''

Revision as of 15:44, 16 May 2021

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 0 18,050
1 2 3 108,698 0 27,596
2 4 7 81,102 0 30,503
3 8 15 50,599 0 23,785
4 16 31 26,814 0 13,631
5 32 63 13,183 0 6,613
6 64 127 6,570 0 3,108
7 128 255 3,462 0 1,485
8 256 511 1,977 0 774
9 512 1,023 1,203 0 422
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 0 ?
19 524,288 1,048,575 ? 0 ?
20 1,048,576 ∞ ? 0 ?
unknown 8,000,000 ∞ 62 -1 -

The current nmax = 8,000,000 as of 2024-03-31.

Riesel primes
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