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 1"

From Prime-Wiki
Jump to: navigation, search
(Adding navbox (this page is included))
(markings)
Line 14: Line 14:
 
===Data table===
 
===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.
 
The following table shows the current available ''k''-values in this Wiki and the targeted values shown by W.Keller for any ''m'' ≤ 23.
 +
 +
:<div style="width:4em; background:PaleGreen; display:inline-block;">&nbsp;</div> : completely included in the Wiki
  
 
{| class="wikitable" style="text-align:right;"
 
{| class="wikitable" style="text-align:right;"
Line 54: Line 56:
 
| [[:Category:Riesel prime riesel f17|17]] || 171 || {{Num|{{PAGESINCATEGORY:Riesel prime riesel f17|pages|R}}}} || 35
 
| [[:Category:Riesel prime riesel f17|17]] || 171 || {{Num|{{PAGESINCATEGORY:Riesel prime riesel f17|pages|R}}}} || 35
 
|-
 
|-
−
| [[:Category:Riesel prime riesel f18|18]] || 136 || {{Num|{{PAGESINCATEGORY:Riesel prime riesel f18|pages|R}}}} || 25
+
| [[:Category:Riesel prime riesel f18|18]] || 136 || style="width:4em; background:PaleGreen; | {{Num|{{PAGESINCATEGORY:Riesel prime riesel f18|pages|R}}}} || 25
 
|-
 
|-
−
| [[:Category:Riesel prime riesel f19|19]] || 111 || {{Num|{{PAGESINCATEGORY:Riesel prime riesel f19|pages|R}}}} || 22
+
| [[:Category:Riesel prime riesel f19|19]] || 111 || style="width:4em; background:PaleGreen; | {{Num|{{PAGESINCATEGORY:Riesel prime riesel f19|pages|R}}}} || 22
 
|-
 
|-
−
| [[:Category:Riesel prime riesel f20|20]] || 89 || {{Num|{{PAGESINCATEGORY:Riesel prime riesel f20|pages|R}}}} || 18
+
| [[:Category:Riesel prime riesel f20|20]] || 89 || style="width:4em; background:PaleGreen; | {{Num|{{PAGESINCATEGORY:Riesel prime riesel f20|pages|R}}}} || 18
 
|-
 
|-
−
| [[:Category:Riesel prime riesel f21|21]] || 71 || {{Num|{{PAGESINCATEGORY:Riesel prime riesel f21|pages|R}}}} || 13
+
| [[:Category:Riesel prime riesel f21|21]] || 71 || style="width:4em; background:PaleGreen; | {{Num|{{PAGESINCATEGORY:Riesel prime riesel f21|pages|R}}}} || 13
 
|-
 
|-
−
| [[:Category:Riesel prime riesel f22|22]] || 58 || {{Num|{{PAGESINCATEGORY:Riesel prime riesel f22|pages|R}}}} || 8
+
| [[:Category:Riesel prime riesel f22|22]] || 58 || style="width:4em; background:PaleGreen; | {{Num|{{PAGESINCATEGORY:Riesel prime riesel f22|pages|R}}}} || 8
 
|-
 
|-
−
| [[:Category:Riesel prime riesel f23|23]] || 50 || {{Num|{{PAGESINCATEGORY:Riesel prime riesel f23|pages|R}}}} || &ge; 1
+
| [[:Category:Riesel prime riesel f23|23]] || 50 || style="width:4em; background:PaleGreen; | {{Num|{{PAGESINCATEGORY:Riesel prime riesel f23|pages|R}}}} || &ge; 1
 
|-
 
|-
−
| [[:Category:PrimeGrid Riesel Problem|unknown]] || 49 || {{Num|{{#expr:{{PAGESINCATEGORY:PrimeGrid Riesel Problem|pages|R}}-1}}}} || 0
+
| [[:Category:PrimeGrid Riesel Problem|unknown]] || 49 || style="width:4em; background:PaleGreen; | {{Num|{{#expr:{{PAGESINCATEGORY:PrimeGrid Riesel Problem|pages|R}}-1}}}} || 0
 
|}
 
|}
  

Revision as of 17:39, 2 August 2020

Logo.svg This article is only a stub. You can help PrimeWiki by expanding it.

The Riesel problem consists in 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 which 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 the Wiki
m remain current target
0 254,601 0 39,867
1 214,734 0 59,460
2 155,274 0 62,311
3 92,963 0 45,177
4 47,786 0 24,478
5 23,308 0 11,668
6 11,640 0 5,360
7 6,280 0 2,728
8 3,552 0 1,337
9 2,215 0 785
10 1,430 0 467
11 963 0 289
12 674 0 191
13 483 0 125
14 358 0 87
15 271 0 62
16 209 0 38
17 171 0 35
18 136 0 25
19 111 0 22
20 89 0 18
21 71 0 13
22 58 0 8
23 50 0 ≥ 1
unknown 49 -1 0

Notes

  1. ↑ Riesel problem by Wilfrid Keller

See also

External links

Riesel primes
Retrieved from "https://www.rieselprime.de/z/index.php?title=Riesel_problem_1&oldid=10251"