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Difference between revisions of "Riesel problem 1"

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{| class="wikitable" style="text-align:right;"
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!{{V|m}}!!remain!!current!!target
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!{{V|m}}!!{{Vn}}<sub>min</sub>!!{{Vn}}<sub>max</sub>!!remain!!current!!target
 
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| [[:Category:Riesel prime riesel f0|0]] || {{Num|254601}} || {{Num|{{PAGESINCATEGORY:Riesel prime riesel f0|pages|R}}}} || {{Num|39867}}
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| [[:Category:Riesel prime riesel f0|0]] || 1 || 1 || {{Num|254601}} || {{Num|{{PAGESINCATEGORY:Riesel prime riesel f0|pages|R}}}} || {{Num|39867}}
 
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| [[:Category:Riesel prime riesel f1|1]] || {{Num|214734}} || {{Num|{{PAGESINCATEGORY:Riesel prime riesel f1|pages|R}}}} || {{Num|59460}}
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| [[:Category:Riesel prime riesel f1|1]] || 2 || 3 || {{Num|214734}} || {{Num|{{PAGESINCATEGORY:Riesel prime riesel f1|pages|R}}}} || {{Num|59460}}
 
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| [[:Category:Riesel prime riesel f2|2]] || {{Num|155274}} || {{Num|{{PAGESINCATEGORY:Riesel prime riesel f2|pages|R}}}} || {{Num|62311}}
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| [[:Category:Riesel prime riesel f2|2]] || 4 || 7 || {{Num|155274}} || {{Num|{{PAGESINCATEGORY:Riesel prime riesel f2|pages|R}}}} || {{Num|62311}}
 
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| [[:Category:Riesel prime riesel f3|3]] || {{Num|92963}} || {{Num|{{PAGESINCATEGORY:Riesel prime riesel f3|pages|R}}}} || {{Num|45177}}
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| [[:Category:Riesel prime riesel f3|3]] || 8 || 15 || {{Num|92963}} || {{Num|{{PAGESINCATEGORY:Riesel prime riesel f3|pages|R}}}} || {{Num|45177}}
 
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| [[:Category:Riesel prime riesel f4|4]] || {{Num|47786}} || {{Num|{{PAGESINCATEGORY:Riesel prime riesel f4|pages|R}}}} || {{Num|24478}}
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| [[:Category:Riesel prime riesel f4|4]] || 16 || 31 || {{Num|47786}} || {{Num|{{PAGESINCATEGORY:Riesel prime riesel f4|pages|R}}}} || {{Num|24478}}
 
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| [[:Category:Riesel prime riesel f5|5]] || {{Num|23308}} || {{Num|{{PAGESINCATEGORY:Riesel prime riesel f5|pages|R}}}} || {{Num|11668}}
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| [[:Category:Riesel prime riesel f5|5]] || 32 || 63 || {{Num|23308}} || {{Num|{{PAGESINCATEGORY:Riesel prime riesel f5|pages|R}}}} || {{Num|11668}}
 
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| [[:Category:Riesel prime riesel f6|6]] || {{Num|11640}} || {{Num|{{PAGESINCATEGORY:Riesel prime riesel f6|pages|R}}}} || {{Num|5360}}
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| [[:Category:Riesel prime riesel f6|6]] || 64 || 127 || {{Num|11640}} || {{Num|{{PAGESINCATEGORY:Riesel prime riesel f6|pages|R}}}} || {{Num|5360}}
 
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| [[:Category:Riesel prime riesel f7|7]] || {{Num|6280}} || {{Num|{{PAGESINCATEGORY:Riesel prime riesel f7|pages|R}}}} || {{Num|2728}}
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| [[:Category:Riesel prime riesel f7|7]] || 128 || 255 || {{Num|6280}} || {{Num|{{PAGESINCATEGORY:Riesel prime riesel f7|pages|R}}}} || {{Num|2728}}
 
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| [[:Category:Riesel prime riesel f8|8]] || {{Num|3552}} || {{Num|{{PAGESINCATEGORY:Riesel prime riesel f8|pages|R}}}} || {{Num|1337}}
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| [[:Category:Riesel prime riesel f8|8]] || 256 || 511 || {{Num|3552}} || {{Num|{{PAGESINCATEGORY:Riesel prime riesel f8|pages|R}}}} || {{Num|1337}}
 
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| [[:Category:Riesel prime riesel f9|9]] || {{Num|2215}} || {{Num|{{PAGESINCATEGORY:Riesel prime riesel f9|pages|R}}}} || 785
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| [[:Category:Riesel prime riesel f9|9]] || 512 || {{Num|1023}} || {{Num|2215}} || {{Num|{{PAGESINCATEGORY:Riesel prime riesel f9|pages|R}}}} || 785
 
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| [[:Category:Riesel prime riesel f10|10]] || {{Num|1430}} || {{Num|{{PAGESINCATEGORY:Riesel prime riesel f10|pages|R}}}} || 467
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| [[:Category:Riesel prime riesel f10|10]] || {{Num|1024}} || {{Num|2047}} || {{Num|1430}} || {{Num|{{PAGESINCATEGORY:Riesel prime riesel f10|pages|R}}}} || 467
 
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| [[:Category:Riesel prime riesel f11|11]] || 963 || {{Num|{{PAGESINCATEGORY:Riesel prime riesel f11|pages|R}}}} || 289
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| [[:Category:Riesel prime riesel f11|11]] || {{Num|2048}} || {{Num|4095}} || 963 || {{Num|{{PAGESINCATEGORY:Riesel prime riesel f11|pages|R}}}} || 289
 
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| [[:Category:Riesel prime riesel f12|12]] || 674 || {{Num|{{PAGESINCATEGORY:Riesel prime riesel f12|pages|R}}}} || 191
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| [[:Category:Riesel prime riesel f12|12]] || {{Num|4096}} || {{Num|8191}} || 674 || {{Num|{{PAGESINCATEGORY:Riesel prime riesel f12|pages|R}}}} || 191
 
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| [[:Category:Riesel prime riesel f13|13]] || 483 || style="width:4em; background:PaleGreen; | 125 || 125
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| [[:Category:Riesel prime riesel f13|13]] || {{Num|8192}} || {{Num|16383}} || 483 || style="width:4em; background:PaleGreen; | 125 || 125
 
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| [[:Category:Riesel prime riesel f14|14]] || 358 || style="width:4em; background:PaleGreen; | 87 || 87
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| [[:Category:Riesel prime riesel f14|14]] || {{Num|16384}} || {{Num|32767}} || 358 || style="width:4em; background:PaleGreen; | 87 || 87
 
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| [[:Category:Riesel prime riesel f15|15]] || 271 || style="width:4em; background:PaleGreen; | 62 || 62
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| [[:Category:Riesel prime riesel f15|15]] || {{Num|32768}} || {{Num|65535}} || 271 || style="width:4em; background:PaleGreen; | 62 || 62
 
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| [[:Category:Riesel prime riesel f16|16]] || 209 || style="width:4em; background:PaleGreen; | 38 || 38
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| [[:Category:Riesel prime riesel f16|16]] || {{Num|65536}} || {{Num|131071}} || 209 || style="width:4em; background:PaleGreen; | 38 || 38
 
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| [[:Category:Riesel prime riesel f17|17]] || 171 || style="width:4em; background:PaleGreen; | 35 || 35
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| [[:Category:Riesel prime riesel f17|17]] || {{Num|131072}} || {{Num|262143}} || 171 || style="width:4em; background:PaleGreen; | 35 || 35
 
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| [[:Category:Riesel prime riesel f18|18]] || 136 || style="width:4em; background:PaleGreen; | 25 || 25
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| [[:Category:Riesel prime riesel f18|18]] || {{Num|262144}} || {{Num|524287}} || 136 || style="width:4em; background:PaleGreen; | 25 || 25
 
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| [[:Category:Riesel prime riesel f19|19]] || 111 || style="width:4em; background:PaleGreen; | 22 || 22
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| [[:Category:Riesel prime riesel f19|19]] || {{Num|524288}} || {{Num|1048575}} || 111 || style="width:4em; background:PaleGreen; | 22 || 22
 
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| [[:Category:Riesel prime riesel f20|20]] || 89 || style="width:4em; background:PaleGreen; | 18 || 18
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| [[:Category:Riesel prime riesel f20|20]] || {{Num|1048576}} || {{Num|2097151}} || 89 || style="width:4em; background:PaleGreen; | 18 || 18
 
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| [[:Category:Riesel prime riesel f21|21]] || 71 || style="width:4em; background:PaleGreen; | 13 || 13
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| [[:Category:Riesel prime riesel f21|21]] || {{Num|2097152}} || {{Num|4194303}} || 71 || style="width:4em; background:PaleGreen; | 13 || 13
 
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| [[:Category:Riesel prime riesel f22|22]] || 58 || style="width:4em; background:PaleGreen; | 8 || 8
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| [[:Category:Riesel prime riesel f22|22]] || {{Num|4194304}} || {{Num|8388607}} || 58 || style="width:4em; background:PaleGreen; | 8 || 8
 
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| [[:Category:Riesel prime riesel f23|23]] || 50 || style="width:4em; background:PaleGreen; | 1 || &ge; 1
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| [[:Category:Riesel prime riesel f23|23]] || {{Num|8388608}} || {{Num|16777215}} || 50 || style="width:4em; background:PaleGreen; | 1 || &ge; 1
 
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| [[:Category:PrimeGrid Riesel Problem|unknown]] || 49 || style="width:4em; background:PaleGreen; | {{Num|{{#expr:{{PAGESINCATEGORY:PrimeGrid Riesel Problem|pages|R}}-1}}}} || 0
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| [[:Category:PrimeGrid Riesel Problem|unknown]] || {{Num|16777216}} || &infin; || 49 || style="width:4em; background:PaleGreen; | {{Num|{{#expr:{{PAGESINCATEGORY:PrimeGrid Riesel Problem|pages|R}}-1}}}} || 0
 
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|}
  

Revision as of 12:51, 22 September 2020

The Riesel problem involves determining the smallest Riesel number.

Explanations

In 1956, Hans Riesel showed that there are an infinite number of integers k such that k•2n-1 is not prime for any integer n. He showed that the number k = 509,203 has this property. It is conjectured that this k is the smallest such number that has this property. To prove this, it suffices to show that there exists a value n such that k•2n-1 is prime for each k < 509,203.

Currently, there are -1 k-values smaller than 509,203 that have no known prime. These are reserved by the PrimeGrid Riesel Problem search.

Frequencies

Definition

Let fm define the number of k-values (k < 509,203, odd k, 254,601 candidates) with a first prime of k•2n-1 with n in the interval 2m ≤ n < 2m+1 [1].

Data table

The following table shows the current available k-values in this Wiki and the targeted values shown by W.Keller for any m ≤ 23.

 
 : completely included in Prime-Wiki
m nmin nmax remain current target
0 1 1 254,601 0 39,867
1 2 3 214,734 0 59,460
2 4 7 155,274 0 62,311
3 8 15 92,963 0 45,177
4 16 31 47,786 0 24,478
5 32 63 23,308 0 11,668
6 64 127 11,640 0 5,360
7 128 255 6,280 0 2,728
8 256 511 3,552 0 1,337
9 512 1,023 2,215 0 785
10 1,024 2,047 1,430 0 467
11 2,048 4,095 963 0 289
12 4,096 8,191 674 0 191
13 8,192 16,383 483 125 125
14 16,384 32,767 358 87 87
15 32,768 65,535 271 62 62
16 65,536 131,071 209 38 38
17 131,072 262,143 171 35 35
18 262,144 524,287 136 25 25
19 524,288 1,048,575 111 22 22
20 1,048,576 2,097,151 89 18 18
21 2,097,152 4,194,303 71 13 13
22 4,194,304 8,388,607 58 8 8
23 8,388,608 16,777,215 50 1 ≥ 1
unknown 16,777,216 ∞ 49 -1 0

Notes

  1. ↑ Riesel problem by Wilfrid Keller

See also

External links

Riesel primes
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