Bases > 1030 and k's > CK

[gd_barnes]

Use this thread for reporting reservations/statuses/primes for bases > 1030 or for k's > the conjectured k of bases <= 1030.

Note that these efforts will be outside the scope of the project and will not be formally shown anywhere.

[Batalov]

I have tested R1031, CK 44. 3k remain at n=25,000.
I would like to reserve it to 50K.

:::pl_trivial.txt:::
6
16
26
36
:::pl_prime.txt:::
2*1031^1722-1
12*1031^22-1
18*1031^3-1
20*1031^2-1
24*1031^2-1
28*1031^1-1
30*1031^3-1
32*1031^42-1
34*1031^1-1
38*1031^10-1
42*1031^236-1
22*1031^2897-1
40*1031^4273-1
14*1031^16166-1
:::pl_remain.txt:::
4*1031^n-1
8*1031^n-1
10*1031^n-1

[10metreh]

Just for fun, I decided to see what the conjectured Riesel and Sierp ks for base 65535 would be. As bases 3 (4-1) and 15 (16-1 = 2^4-1) have very high conjectured ks, I reasoned that 65535 (2^16-1) might also have a high conjecture. And finding a Riesel or Sierp k at all was harder than one might think, as the conjectures (which may not be the lowest) and covering sets show:

Riesel:
Conjectured k: 929606540198368
Covering set: {13, 37, 61, 193, 877, 22253377}
Period: 12

Sierp:
Conjectured k: 10766873647286
Covering set: {13, 37, 61, 193, 1657, 22253377}
Period: 12

The Riesel conjecture beats R280 for highest conjectured k, but I haven't searched very far so there might be a smaller one.
Anyone want to see if there are any smaller Riesel or Sierp ks? (I can't be bothered )

[Batalov]

A small update: At n<=75,000, R1031 still had 3 k's. I stopped it.

S1031 has CK=302 and about a dozen k's after the script. Didn't run it.

[10metreh]

Attached are lists of the conjectured ks for the bases from 1031 to 1500.
I've tested all the bases with a CK of 4 to 2.5K (can't be bothered to go further as it's outside the scope of the project), and out of those, only 8 conjectures still have ks remaining. The work done on those bases is also attached (in the ck4 folder).

[nuggetprime]

Originally Posted by Batalov

I have tested R1031, CK 44. 3k remain at n=25,000.
I would like to reserve it to 50K.

:::pl_trivial.txt:::
6
16
26
36
:::pl_prime.txt:::
2*1031^1722-1
12*1031^22-1
18*1031^3-1
20*1031^2-1
24*1031^2-1
28*1031^1-1
30*1031^3-1
32*1031^42-1
34*1031^1-1
38*1031^10-1
42*1031^236-1
22*1031^2897-1
40*1031^4273-1
14*1031^16166-1
:::pl_remain.txt:::
4*1031^n-1
8*1031^n-1
10*1031^n-1

Off topic, but why is 6 not the conjectured k for R1031 if it has trivial factors?

[gd_barnes]

Originally Posted by nuggetprime

Off topic, but why is 6 not the conjectured k for R1031 if it has trivial factors?

It has only one trivial factor for all n-values: 5.

To be the conjectured k, a k must have two or more trivial factors to make the full covering set.

[10metreh]

Originally Posted by 10metreh

Attached are lists of the conjectured ks for the bases from 1031 to 1500.
I've tested all the bases with a CK of 4 to 2.5K (can't be bothered to go further as it's outside the scope of the project), and out of those, only 8 conjectures still have ks remaining. The work done on those bases is also attached (in the ck4 folder).

Found a better k (496311327760) for S1150 - missed it the first time because I only tested for primes up to 1e6 in the covering set and the new k has 1321351 in the set.
Here's an updated list of Sierp conjectures.

[10metreh]

Here are the conjectured ks for bases 1501 to 2048.

[Siemelink]

Originally Posted by Batalov

A small update: At n<=75,000, R1031 still had 3 k's. I stopped it.

I've also worked on base 1031, before I found the thread. Unsurprisngly, I found the same primes. After finding this thread, I skipped 25,000 < n < 75,000. And I was lucky:

Primality testing 10*1031^77187-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 11, base 1+sqrt(11)
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
10*1031^77187-1 is prime! (13348.8097s+0.0557s)

that leaves
4*1031^n-1
8*1031^n-1

I'll take these to n = 100,000.

Willem.

[MyDogBuster]

I'd like to reserve Riesel & Sierp bases 1100-1199. Something to do in my spare time.