Bases 33-100 reservations/statuses/primes

[gd_barnes]

Originally Posted by KEP

Hi Robert

Could you do me a favor and come up with the lowest conjectured value for all base <=2^10 or <=1024? I've a dream and hope to see all the conjectures for bases<=1024 to be taken to n<=50M or proven before I turn hundred... it gives us almost 74 years to reach that goal and with the help of primegrid I actually think it will be possible to take all those conjectures up to n<=50M in maybe less than 74 years. However it requires new scripts to do the initial testings, and a lot more people to desire to work on producing and storing the primes for later construction of proofs. But you think that you can produce the lowest conjecture value for all bases <=1024 and their covering sets?

Just hope that Gary is up for the extra load of work... anyway I'm most likely going to do something else besides the conjectures for a while, and when (if) I return, I'm gonna see how goes with the base 3 conjectures

KEP!

Not possible, even if you assume a doubling of computer speeds every 2 years, which is highly unlikely! You are forgetting that base 1000 for 1000^50000000 is a much larger test than 2^50000000. Even so, taking all k's on Riesel base 2 up to n=50M will be a serious challenge in most of our lifetimes.

Yep, I'll find time to update the web pages. It might be a couple of months before I get all this info. in there but it will get there.

There's one thing that I want to bring up here: Neither I nor anyone else here can claim ownership of these conjectures. This project has only been intended to organize such efforts towards the conjectures not being worked on by others, not own them. We will not be offended if anyone wants to break off and create a separate project for a specific base or two. The base 5 project has made HUGE progress on its own in a few short years on an extremely tough base and personally, I'm glad that they have done it so that we don't need to. The same applies to Sierp base 4.

KEP, you really enjoy base 3 so if you want to create a separate project for it, go right ahead. I'll be glad to assist with that. One guarantee: It's a lot more work to administer these things than you'll ever imagine in the beginning.

All of that said, if another effort is 'dropping the ball' such as has happened with RieselSieve, you can bet we will step in and pick up the slack if the effort goes dormant for too long and there has been little communication about when it will start up again. But if the effort subsequently 'comes back', we'll gladly let them pick it back up again and communicate any progress made.


Gary

[gd_barnes]

Originally Posted by kar_bon

Y.Gallot stated in the paper (don't know were to find) "ON THE NUMBER OF PRIMES IN A SEQUENCE" in 2001 for the Sierpinski conjecture:


and for the Riesel problem he stated:


the smallest not tested exponents for Riesel are at about n=2.3M (so about 2^21)!

just an idea of time for only one conjecture!

Very interesting odds Karsten! It's even more difficult than what I had attempted to compute in another thread, which had the Riesel base 2 conjecture with a better than 50-50 chance of being solved by n=16T (n=16*10^12). That is, I had computed that there should be < 0.5 of a k remaining at that point.

I've now realized that there's one large error that I made in my computations. I assumed the primes would continue to come at the same exponential reducing rate. That is an incorrect assumption because the k's remaining will have respectively less average weight than the k's where primes have been already found. Therefore I'm sure that Gallot's estimate is far more accurate.

Edit: In KEP's defense here, he did not state that the conjectures needed to be proven to realize his dream; only that they need be tested to n=50M. That seems to be a reasonable goal for Riesel base 2 in most of our lifetimes but not for 2046 bases, i.e. 2 bases each for 2 thru 1024! :-)


Gary

[robert44444uk]

Originally Posted by R. Gerbicz

Better Riesel values, also up to base=1024:
http://robert.gerbicz.googlepages.com/riesel.txt

Saved me the work!

Robert - could you disclose to what cover these are tested. Your program requires every cover to be tested. For example it is possible (but unlikely) for a 5-cover to be smallest.

[robert44444uk]

Robert G's list produces lower values than Siemelink's as follows:

66     101954772
71     1132052528
120    166616308
127    93902377422
156    2113322677
175    278467080
195    582483712
238    5415261
240    2952972
280    513613045571841
303    85368
323    93896
325    112882226
345    1295243216
358    27606383
435    31732727570
453    4658266
511    40789000085994
525    8364188
541    15546458
570    12511182
591    30820
661    2518794379382
685    518792
728    212722
777    23485096
796    27199220
799    1885767686976
801    40381102
826    131420459393
855    7419914968008
876    51768432
906    171998037
910    5005381602981
946    2156122023
960    61681833328
963    22349616
966    699327630
981    112303013130
1020   94655888

[kar_bon]

LLR-tested for all k's upto n=6050
sieved to 3.9B=3.9*10^9
124 primes found so far (from 1559)
5.4M candidates left

[gd_barnes]

Originally Posted by kar_bon

LLR-tested for all k's upto n=6050
sieved to 3.9B=3.9*10^9
124 primes found so far (from 1559)
5.4M candidates left

In order to update the web page, I'll need to get a list of the primes. Otherwise, the highest primes list will be out of sync with the n-range tested.

I'll create a page of the k's remaining at n=5K from Willem's earlier posted list a little later today.

[R. Gerbicz]

Originally Posted by robert44444uk

Saved me the work!

Robert - could you disclose to what cover these are tested. Your program requires every cover to be tested. For example it is possible (but unlikely) for a 5-cover to be smallest.

In fact if you test for example exponent=36, then the program will find all coversets (for the listed primes) not only for period=36 but also for the divisors of 36, so for period=2,3,4,6,9,12,18,36.

As I remember I tested for exponent=144 but for low limit for primes (limit=10000), after it was switched to test exponent=8,24,36,48 for large limit. But today I think it was really unnecessary, here it is a quick stat for the Sierpinski side b=2-1024:

number of period=2 is 525
number of period=3 is 53
number of period=4 is 224
number of period=6 is 107
number of period=8 is 18
number of period=9 is 2
number of period=12 is 75
number of period=16 is 1
number of period=18 is 2
number of period=24 is 11
number of period=36 is 2
number of period=48 is 1
number of period=72 is 1
number of period=144 is 1
max prime in coverset=731881 at b=855

And for Riesel side b=2-1024:

number of period=2 is 528
number of period=3 is 53
number of period=4 is 230
number of period=6 is 105
number of period=8 is 23
number of period=10 is 2
number of period=12 is 63
number of period=16 is 1
number of period=18 is 1
number of period=24 is 9
number of period=36 is 5
number of period=48 is 1
number of period=144 is 1
max prime in coverset=921601 at b=959

Yesterday there was a very large prime in one of the coverset, about 300million, but I found a lower k value for that. Seeing this table it is more than enough to search only for primelimit=1M or 2M.

I would be glad if some of you could find a better k value.

[gd_barnes]

Originally Posted by Siemelink

Hi everyone,

I've double checked my work on the Riesel 35 Conjecture. The value is 287860. I've taken the k's to n=200 with PFGw. Then I sorted out the multiples of 35 and the squares. ThenI took the remainder to n=5000
I've attached the 1559 k's that I had left.
The top ten primes list is this:
65216 4986
248264 4980
104690 4978
126050 4978
286652 4976
129052 4975
229454 4974
48772 4965
169448 4964
7874 4962

All the primes are in a file that zips to 350k, that doesn't fit on the forum. The can be sent if so desired.

Willem.

Willem,

Can you send me all your primes on Riesel base 35?


Thanks,
Gary

[gd_barnes]

Originally Posted by kar_bon

LLR-tested for all k's upto n=6050
sieved to 3.9B=3.9*10^9
124 primes found so far (from 1559)
5.4M candidates left

Karsten,

Per your Email showing primes found up to n=6060, I have now listed all k's remaining and highest primes found for Riesel base 35.

Willem,

Your list of k's remaining for this base had a slight error in it. You had both k=94 and 115150 remaining. Since 115150=94*35^2, it can be eliminated. The list of primes that you found will help me do a little more verification.

Karsten,

You can eliminate k=115150 from your testing. The web pages reflect the removal. Once you do that, you might check your file to verify that there are 1434 k's remaining at n=6060.


Gary

[robert44444uk]

Originally Posted by R. Gerbicz

Yesterday there was a very large prime in one of the coverset, about 300million, but I found a lower k value for that. Seeing this table it is more than enough to search only for primelimit=1M or 2M.

I would be glad if some of you could find a better k value.

I ran both Sierpinski and Riesel to 1024 with 12-cover and using all primes less than 10 million and no better values were found. I plan to look at 7 or 8 very high k-candidates to see if they can be bettered

[gd_barnes]

Originally Posted by 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.

Per Robert Gerbicz's improved Riesel list, the conjecture for Riesel base 48 is k=3226 with a covering set of {5, 7, 461}. I have now confirmed it.

This reduces the k's remaining at n=10K from 74 to 55 and changed the top 10 primes. The web pages will be updated accordingly.

I checked his list vs. what we show up to Riesel base 50 and that was the only incorrect conjecture that I found.


Gary