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 |
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 |
125 |
125
|
| 14 |
358 |
87 |
87
|
| 15 |
271 |
62 |
62
|
| 16 |
209 |
38 |
38
|
| 17 |
171 |
35 |
35
|
| 18 |
136 |
25 |
25
|
| 19 |
111 |
22 |
22
|
| 20 |
89 |
18 |
18
|
| 21 |
71 |
13 |
13
|
| 22 |
58 |
8 |
8
|
| 23 |
50 |
1 |
≥ 1
|
| unknown |
49 |
-1 |
0
|
Notes
See also
External links
