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Difference between revisions of "Riesel problem 1"
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Revision as of 14:41, 5 August 2020
The Riesel problem consists in 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 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.
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 | 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
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