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Riesel problem 1

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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 2mn < 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 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

Riesel primes