A Sierpinski/Riesel-like problem

[sweety439]

Originally Posted by sweety439

(20543*108^3375+1)/107 is prime

3 k's for R108 are still remain ....

Still no prime found for these 3 k's, they are likely tested to n>=6000

Also see post #341 for the primes at n=1K=2K for S/R 108

[sweety439]

We can use the sense of http://www.iakovlev.org/zip/riesel2.pdf to conclude that (k*b^n+c)/gcd(k+c,b-1) (k>=1, b>=2, c != 0, gcd(k,c) = 1, gcd(b,c) = 1) eventually should yield a prime, when it does not have primes for small n>=1

We should find the n's such that (k*b^n+c)/gcd(k+c,b-1) does not have small prime factors (and the znorder of b mod its prime factors are also not small), nor has algebra factors (i.e. k*b^n and -c are both rth powers for some r>1, or k*b^n*c is of the form 4*m^4)

[sweety439]

Update pdf files for the Sierpinski/Riesel conjectures

[sweety439]

Originally Posted by sweety439

Update current status file for R/S 40

Update newest status text file for R/S 40

[sweety439]

Riesel base 2021 is proven!!! With CK=13, see https://github.com/xayahrainie4793/E...0to%202048.txt

k,n
1,67
2,1048
3,1773
4,3
5,140
6,2
7,117
8,2
9,1
10,269
11,14
12,1

Interestingly, the prime for k=2 and k=3 are both large.

[kar_bon]

So you got your own definition of GCD?

In the first post reads (for Riesel side): (k*b^n-1)/gcd(k-1, b-1)

b=2021, k=1, n=67 (from table above)

GCD for k=1 in the above formula is undefined and so (1*2021^67-1)/2020 is prime but do not correlates to your definiton of the problem and the definition of GCD.

[sweety439]

Originally Posted by kar_bon

So you got your own definition of GCD?

In the first post reads (for Riesel side): (k*b^n-1)/gcd(k-1, b-1)

b=2021, k=1, n=67 (from table above)

GCD for k=1 in the above formula is undefined and so (1*2021^67-1)/2020 is prime but do not correlates to your definiton of the problem and the definition of GCD.

See https://en.wikipedia.org/wiki/Greatest_common_divisor, gcd(a, 0) = |a|, for a ≠ 0, since any number is a divisor of 0, and the greatest divisor of a is |a|. This is usually used as the base case in the Euclidean algorithm. The GCD is 2020 for all k == 1 mod 2020, including k = 1

[sweety439]

Update the status of Riesel problems to include the new primes for R2 and new test limits for R2, R6 (k=1597), R108 (k = 5351, 6528, 13162)

[sweety439]

Update the status of Sierpinski problems to include the new primes for S80 (all k except k=947), S81, S108 (k=20543) and the new test limits for S2, S80 (all k except k=947), S81, S97

[sweety439]

Upload pdf files for these conjectures

[sweety439]

Originally Posted by sweety439

1,3
2,228
3,1
4,1
5,2
6,1
7,1
8,2
9,1
10,1
11,2
12,1
13,1
14,10
15,3
16,3
17,2
18,1
19,3
20,26
21,4
22,1
23,4
24,1
25,1
26,2
27,2
28,1
29,2
30,8
31,1
32,316
33,2
34,11
35,2
36,15
37,1
38,4
39,2
40,67
41,14
42,1
43,1
44,4
45,1
46,1
47,2
48,1
49,103
50,328
51,1
52,549
53,46
54,1
55,153
56,4
57,2
58,1
59,36
60,2
61,1
62,4
63,3
64,1

With CK=65

Conjecture proven

searched to n=2000, see the text file for the status, 0 if no (probable) prime found for this k

CK=3259

Only list k == 1 mod 7 and k == 1 mod 23 since other k are already in CRUS