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Generalized Prime Riesel Conjectures

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Hi everyone,

Here is what I have been busy with for the last few months. I've been trying to prove conjectures that are prime and then only the k's that are prime.
For base 2 that is the same as the existing Prime Riesel Prime search. I've been looking at those with other bases:

base primeRiesel
2...........509,203
4...........2,251,349
6...........429,127
8...........307.........Proven
10..........72,953
12..........6,397
14..........11..........Proven
16..........313,517
18..........1,481......Proven
20..........13..........Proven
22..........93,701
24..........335,411
26..........149.........Proven
28..........231,419
30..........11,471
32..........23..........Proven
34..........29..........Proven
36..........429,127
38..........13..........Proven
40..........42,970,133
42..........15,137
44..........11..........Proven
46..........288,203
48..........8,807
50..........67

I've attached my result sheet, that's easier to read. A natural location for this would be on Gary's CRUS page. But I haven't gone all out on the double checking, so the contents may be not 100% correct.

Enjoy, Willem.

 kar_bon 2008-12-01 10:18

nice table!

for information: i've found data about the extension of the Riesel Prime Conjecture upto n=10^7.
the data includes all first primes 1024<n<30000 for the k's. i'm testing n>30000 and doublecheking all lower values. there're about 5600 k's without a prime for 509203<=k<=10^7 and many k's with Nash weight=0.
when doubleckeck is ok, i'll put a new page on rieselprime.de!

 gd_barnes 2008-12-02 21:27

Very interesting efforts guys.

Karsten, I had attempted such an effort for Riesel base 2 for k=509205-600000 up to n=25K. I have the info. but obviously it's a small duplication of what you are doing.

Willem, I won't easily be able to show your info. on the pages as currently designed. I'll make a note of it on my task list but it will likely be several months before I'm able to get to it.

In the mean time, I've done some searches for Riesel bases 50-125 recently. I'll post a cursory sampling of what I've done in another thread today so that no one duplicates my effort. I chose most of the bases that were relatively easy to prove and a few that will be a little more difficult to keep things interesting.

Gary

 sweety439 2017-05-18 16:52

Are there any project for the generalized prime Sierpinski conjectures?

Of course, for base 2, this CK is 271129.

 sweety439 2017-05-23 18:44

[QUOTE=sweety439;459280]Are there any project for the generalized prime Sierpinski conjectures?

Of course, for base 2, this CK is 271129.[/QUOTE]

base primeSierpinski
2.........271129
4.........271129
6.........7075837
8.........47.............Proven
10.......48247
12.......521...........Proven
14.......11.............Proven
16.......3608251
18.......571...........Proven
20.......13.............Proven

 sweety439 2017-06-19 15:41

@Gary, do you decide to solve the generalized prime Sierpinski/Riesel conjectures?

 sweety439 2020-08-05 00:11

Found more CK:

Prime Sierpinski:

[CODE]
b,CK
2,271129
4,271129
6,282001
8,47
10,48247
12,521
14,11
16,2202997
18,571
20,13
22,30727
24,534301
26,1627
28,8293
30,18973
32,23
34,181
36,11093
38,53
40,826477
42,350881
44,11
46,51511
48,5531
50,67
52,260761
54,89
56,37
58,211573
60,199103
62,13
64,79
[/CODE]

Prime Riesel:

[CODE]
b,CK
2,509203
4,2251349
6,429127
8,307
10,72953
12,6397
14,11
16,313517
18,1481
20,13
22,93701
24,335411
26,149
28,231419
30,11471
32,23
34,29
36,429127
38,13
40,42970133
42,15137
44,11
46,288203
48,8807
50,67
52,599429
54,89
56,37
58,1429451
60,1013819
62,13
64,311
[/CODE]

(I searched to k=5M, and the CK for S40 is given by post #1)

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