Riesel problem 1

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 f_m 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 2^m ≤ n < 2^m+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	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

See also

• PrimeGrid Riesel Problem
• Riesel Sieve

External links

• Riesel number