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Difference between revisions of "Riesel problem 1"
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| [[:Category:Riesel prime riesel f12|12]] || {{Num|4096}} || {{Num|8191}} || 674 || {{Num|{{PAGESINCATEGORY:Riesel prime riesel f12|pages|R}}}} || 191 | | [[:Category:Riesel prime riesel f12|12]] || {{Num|4096}} || {{Num|8191}} || 674 || {{Num|{{PAGESINCATEGORY:Riesel prime riesel f12|pages|R}}}} || 191 | ||
|- | |- | ||
| − | | [[:Category:Riesel prime riesel f13|13]] || {{Num|8192}} || {{Num|16383}} || 483 || style=" | + | | [[:Category:Riesel prime riesel f13|13]] || {{Num|8192}} || {{Num|16383}} || 483 || style="background:PaleGreen; | 125 || 125 |
|- | |- | ||
| − | | [[:Category:Riesel prime riesel f14|14]] || {{Num|16384}} || {{Num|32767}} || 358 || style=" | + | | [[:Category:Riesel prime riesel f14|14]] || {{Num|16384}} || {{Num|32767}} || 358 || style="background:PaleGreen; | 87 || 87 |
|- | |- | ||
| − | | [[:Category:Riesel prime riesel f15|15]] || {{Num|32768}} || {{Num|65535}} || 271 || style=" | + | | [[:Category:Riesel prime riesel f15|15]] || {{Num|32768}} || {{Num|65535}} || 271 || style="background:PaleGreen; | 62 || 62 |
|- | |- | ||
| − | | [[:Category:Riesel prime riesel f16|16]] || {{Num|65536}} || {{Num|131071}} || 209 || style=" | + | | [[:Category:Riesel prime riesel f16|16]] || {{Num|65536}} || {{Num|131071}} || 209 || style="background:PaleGreen; | 38 || 38 |
|- | |- | ||
| − | | [[:Category:Riesel prime riesel f17|17]] || {{Num|131072}} || {{Num|262143}} || 171 || style=" | + | | [[:Category:Riesel prime riesel f17|17]] || {{Num|131072}} || {{Num|262143}} || 171 || style="background:PaleGreen; | 35 || 35 |
|- | |- | ||
| − | | [[:Category:Riesel prime riesel f18|18]] || {{Num|262144}} || {{Num|524287}} || 136 || style=" | + | | [[:Category:Riesel prime riesel f18|18]] || {{Num|262144}} || {{Num|524287}} || 136 || style="background:PaleGreen; | 25 || 25 |
|- | |- | ||
| − | | [[:Category:Riesel prime riesel f19|19]] || {{Num|524288}} || {{Num|1048575}} || 111 || style=" | + | | [[:Category:Riesel prime riesel f19|19]] || {{Num|524288}} || {{Num|1048575}} || 111 || style="background:PaleGreen; | 22 || 22 |
|- | |- | ||
| − | | [[:Category:Riesel prime riesel f20|20]] || {{Num|1048576}} || {{Num|2097151}} || 89 || style=" | + | | [[:Category:Riesel prime riesel f20|20]] || {{Num|1048576}} || {{Num|2097151}} || 89 || style="background:PaleGreen; | 18 || 18 |
|- | |- | ||
| − | | [[:Category:Riesel prime riesel f21|21]] || {{Num|2097152}} || {{Num|4194303}} || 71 || style=" | + | | [[:Category:Riesel prime riesel f21|21]] || {{Num|2097152}} || {{Num|4194303}} || 71 || style="background:PaleGreen; | 13 || 13 |
|- | |- | ||
| − | | [[:Category:Riesel prime riesel f22|22]] || {{Num|4194304}} || {{Num|8388607}} || 58 || style=" | + | | [[:Category:Riesel prime riesel f22|22]] || {{Num|4194304}} || {{Num|8388607}} || 58 || style="background:PaleGreen; | 8 || 8 |
|- | |- | ||
| − | | [[:Category:Riesel prime riesel f23|23]] || {{Num|8388608}} || {{Num|16777215}} || 50 || style=" | + | | [[:Category:Riesel prime riesel f23|23]] || {{Num|8388608}} || {{Num|16777215}} || 50 || style="background:PaleGreen; | {{PAGESINCATEGORY:Riesel prime riesel f23|pages|R}} || ≥ {{PAGESINCATEGORY:Riesel prime riesel f23|pages|R}} |
|- | |- | ||
| − | | [[:Category:PrimeGrid Riesel Problem|unknown]] || {{Num|16777216}} || ∞ || {{#expr:50-{{PAGESINCATEGORY:Riesel prime riesel f23|pages|R}}}} || style=" | + | | [[:Category:PrimeGrid Riesel Problem|unknown]] || {{Num|16777216}} || ∞ || {{#expr:50-{{PAGESINCATEGORY:Riesel prime riesel f23|pages|R}}}} || style="background:PaleGreen; | {{#expr:{{PAGESINCATEGORY:PrimeGrid Riesel Problem|pages|R}}-1}} || 0 |
|} | |} | ||
'''The current {{Vn}}<sub>max</sub> = {{Num|{{Multi Reservation:11-NMax}}}} as of {{Multi Reservation:11-Date}}.''' | '''The current {{Vn}}<sub>max</sub> = {{Num|{{Multi Reservation:11-NMax}}}} as of {{Multi Reservation:11-Date}}.''' | ||
Revision as of 08:11, 13 May 2021
The Riesel problem involves determining the smallest Riesel number.
Contents
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 | 0 | ≥ 0 |
| unknown | 16,777,216 | ∞ | 50 | -1 | 0 |
The current nmax = 16,034,000 as of 2024-11-12.
Notes
See also
External links
Riesel primes
| Base = 2 : |
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