Bases 33-100 reservations/statuses/primes

[gd_barnes]

Originally Posted by Siemelink

Ah yes, other bases. I wrote a program to calculate conjectures myself. I've also done some more work on the Riesel bases until 50.
Bases 34, 38, 41, 43, 44, 47 and 50 are trivial to prove.
Bases 35, 39, and 40 have conjectures higher than a million.
Bases 36, 37, 42, 45, 46, 48 have between 20 and 100 remaining k at n = 10,000
Base 49 has 1 remaining k. That one I'd like reserved for myself.

Gary, I hadn't mentioned this because I did't want to hand over the data to you and dropping you in a hole like I did with the base 25. I'll post the trivial conjectures when I have them in the same format as the one that I gave last week.
As for the others, tell me how you like the data and I'll format it that way.

Willem.

The format that you did base 33 in was a good one. All k's were accounted for. So if the conjectured-k is not too big, send me a file or spreadsheet of an accounting of all k-values. You don't have to list all that have trivial factors and algebraic factors but a statement as to what those are helps.

In other words, it's best if everything is sorted by k except for the trivial k's. Example on some fictional base:

k==(1 mod 3) is trivial
 
 k prime/status
 2 5
 3 remaining
 5 1
 6 3
 8 2
 9 algebraic factors
11 remaining
etc. up to the conjectured k-value

This accounts for everything in a nutshell. Alternatively, if the algebraic factors are very consistent (which they frequently are not like on base 33), you can just state something like "k's that are a perfect square have algebraic factors" and not show those in the list of k's.


Gary

[Siemelink]

1394*49^52698-1
1266*49^36191-1
230*49^24824-1
1706*49^16337-1
1784*49^13480-1
786*49^6393-1

I am running PFGW on these at the moment, the confirmation will follow later.

Willem.

[gd_barnes]

Originally Posted by Siemelink

1394*49^52698-1
1266*49^36191-1
230*49^24824-1
1706*49^16337-1
1784*49^13480-1
786*49^6393-1

I am running PFGW on these at the moment, the confirmation will follow later.

Willem.

Wow; you've put in some serious work on this one! It looks like you noticed that I did a preliminary search on the base as a check like I do on all of them. Usually I only go to n=2K but I couldn't believe that there were still so many k's remaining so I went to n=5K thinking I might have the wrong conjectured value. I was going to post a note questioning you only having one k-value remaining when I still had 7 remaining at n=5K but I see that indeed you've knocked them all out except one. That's some serious CPU crunching there to get such a high base past n=50K!

It looks like you may be in top-5000 territory (i.e. n>60K) on the last k. Good luck with it!


Gary

[Siemelink]

Originally Posted by gd_barnes

Wow; you've put in some serious work on this one! It looks like you noticed that I did a preliminary search on the base as a check like I do on all of them.
It looks like you may be in top-5000 territory (i.e. n>60K) on the last k. Good luck with it!

Gary

I could have known that a casually mentioned figure would be picked up by you. No half baked entries on your pages!
By now the six primes were confirmed by PFGW.

Willem.

[Siemelink]

The riesel conjecture for base 48 = 4208, with cover set {7, 13, 37, 61}
Even => 7
6m+1 => 13
6m+3 => 37
6m+5 => 61

checked n upto 10000
total k 4117
total p 4043
Remaining k 74

I've checked the 4043 primes with pfgw, they all hold up. Of the remaining k, two are squares but I couldn't eliminate them. There is one k that can be divided by 48. but I coudn't eliminate that one either.

Top ten primes
1422 9235
3179 9107
1021 8570
4108 8296
3382 7927
1103 7918
475 7424
2449 7244
3907 7083
3541 7078

All the k's and primes are in the attachment. Feel free to find more primes.

Enjoy, Willem.

[Siemelink]

The lowest Riesel for base 39 = 1,352,534, with covering set {5, 7, 223, 1483}.
The lowest Riesel for base 40 = 3,386,517, with covering set {7, 41, 223, 547}.

I've calculated these with my riesel generator, but I didn't generate any k. If you feel like generating a lot of primes, here is your chance.

Willem.

[gd_barnes]

Thanks Willem. Your base 48 info. is exactly what we need on a new base...covering set and all.

One thing I'll add for everyone's reference: Willem has correctly removed all k==(1 mod 47) remaining, which have a trivial factor of...you guessed it...47.


Gary

[gd_barnes]

Willem,

What is your search limit on k=2186 for Sierp base 49 and how high were you going to take it? I have used n=5K because that was how high I searched it to get all of the small primes for the base. I assume you've searched it somewhere above n=50K since you have a prime for k=1394 at n=52698.


Thanks,
Gary

[Siemelink]

Originally Posted by gd_barnes

Willem,

What is your search limit on k=2186 for Sierp base 49 and how high were you going to take it? I have used n=5K because that was how high I searched it to get all of the small primes for the base. I assume you've searched it somewhere above n=50K since you have a prime for k=1394 at n=52698.


Thanks,
Gary

My Riesel 49 effort is at 88,000 and continuing until 100,000. After that I'll see.

Willem.

[Siemelink]

Hi everyone,

here is my effort on Riesel base 46. The conjectured lowest riesel is 8177. The cover set is {29, 47, 73}. While generating the k's I've ignored even k's and k mod 23 = 1. At n = 10,000 there are 22 k's left:
93
800
870
1317
1362
2819
3147
3194
3383
3812
4419
4580
5940
6060
6062
6297
7157
7284
7424
7472
7520
7848

I've checked against squares, there are none left. k = 4278 = 93 *48 and 93 is still in the list. That allows me te remove k = 4278.

The top ten of primes is:
6224 8837
4464 7100
3504 4377
6524 3504
7715 3482
1940 3473
5979 3275
2042 3010
4610 2724
6263 2372


All the primes have been tested with pfgw and are attached. Find some more!

Willem.

[gd_barnes]

Originally Posted by Siemelink

Hi everyone,

here is my effort on Riesel base 46. The conjectured lowest riesel is 8177. The cover set is {29, 47, 73}. While generating the k's I've ignored even k's and k mod 23 = 1.

I assume that you meant that you ignored k==(1 mod 3) and (1 mod 5).

Ignoring k==(1 mod 23) would be for Riesel base 47. We would never ignore even k's.


Gary