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-   -   Bases 33-100 reservations/statuses/primes (https://www.mersenneforum.org/showthread.php?t=10475)

 kar_bon 2008-10-09 08:25

base 35

status for a run over night (one core of Quad):

sieved to p=535M (from 402M) about 90000 candidates less
llr tested upto n=5538 (from 5249) = 20000 pairs tested

31 more primes found = now 1490 k's left (from 1559)

after deletion of these sequences: 6,270,000 candidates all over left (from 6.5M)

to llr-test a candidate it takes about 3.7 s but it's more efficient to find a prime and delete a sequence from the sieve-file (about 5000 candidates for a sequence) as only sieving for now!

 Siemelink 2008-10-09 20:08

Good luck Karsten!

I took base 19 to 30,000. That has a similar amount of remaining k's. It took a long long time. But my PCs are quite old.
Anyway, when I find the time I'll publish the numbers on base 36 as well. I've assigned a core to that, it is up to 22,000 by now, 100 k's left or so.

Willem.

 robert44444uk 2008-10-15 13:33

Just catching up with this thread. FYI, "covering.exe" had an error in it, which invalidated the conjectured lowest Riesel b=43. The error has been corrected but you should get the latest version of covering.exe if you intend further work on higher bases.

I intend to at least list the lowest conjectured covering sets for Sierpinski and Riesel up to b=1000, but the rate these numbers increase by in the power series suggests that very few will be proven, and limitations on bases for prime proving algorithms accentuates. I agree that concentrating on b=3 to 100 is worthwhile.

But the lists may show that the average value of lowest covers decreases, and that is worth looking at.

 KEP 2008-10-15 15:39

[QUOTE=robert44444uk;145447]Just catching up with this thread. FYI, "covering.exe" had an error in it, which invalidated the conjectured lowest Riesel b=43. The error has been corrected but you should get the latest version of covering.exe if you intend further work on higher bases.

I intend to at least list the lowest conjectured covering sets for Sierpinski and Riesel up to b=1000, but the rate these numbers increase by in the power series suggests that very few will be proven, and limitations on bases for prime proving algorithms accentuates. I agree that concentrating on b=3 to 100 is worthwhile.

But the lists may show that the average value of lowest covers decreases, and that is worth looking at.[/QUOTE]

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 :smile:

KEP!

 Siemelink 2008-10-15 20:47

1 Attachment(s)
Ah, like this you mean? I conjured this list with my own program. Any checks/errors would be welcome. I used the primes smaller than 10,000 for the covering sets.

Willem.
--
the only one not in the list is the riesel for base 921. It took too long so I pressed ^C

 KEP 2008-10-16 09:24

[QUOTE=Siemelink;145481]Ah, like this you mean? I conjured this list with my own program. Any checks/errors would be welcome. I used the primes smaller than 10,000 for the covering sets.

Willem.
--
the only one not in the list is the riesel for base 921. It took too long so I pressed ^C[/QUOTE]

Good work Siemelink :smile:

Any chance the 3 conjectures that states x.xxexx, can be conjectured more exact? Also any chance you can make a list for Sierpinski side too? Also I may add, that even in 74 years it is going to be a tough task to reach a milestone of n<=50M for all the billions of k's that needs to be tested at n>25000, but if popularity is going to grow with this project and computer speeds is going to double every second year as it has up to date, we will be able to get at least a great deal towards that goal :smile:

But let me hear the answers for my questions, then we can always discuss future milestones... maybe we also should discuss milestones with a shorter lifeexpectancy :smile:

Regards

KEP

 MrOzzy 2008-10-16 09:51

[quote=Siemelink;145481]Ah, like this you mean? I conjured this list with my own program. Any checks/errors would be welcome. I used the primes smaller than 10,000 for the covering sets.

Willem.
--
the only one not in the list is the riesel for base 921. It took too long so I pressed ^C[/quote]

I've found a better conjecture for Riesel base 71: 1132052528 in stead of 80375729488 like it is listed in the file you supplied. I don't know how to prove the conjecture, I just use the tools I know of. I've checked the factors for all n of base 71 upto n=100. The factors making all results composite are:

3 for all odd n.
13,37,73,109,1657 and 2521 for all even n.

In case I missed something these are the primes considered by covering.exe: 3,5113,2521,1657,37,13,1954357,17,113,577,19,73,109,282439,87553,3889,501841,937,1297,180001

Edit: 75070204388 is also smaller as 80375729488 and has a full covering set, still 1132052528 is better :-)

 kar_bon 2008-10-16 09:57

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:
[quote]
We have a 50% chance of solving Sierpinski problem at N = 2^43 about 10^13.
We have a 5% chance of solving it at N = 2^30 about 10^9.
We have a 95% chance of solving it at N = 2^81 about 10^24.
Note also that the chances at 2^20, 2^21 and 2^22 are respectively about 10^-6, 10^-5 and 10^-4.
[/quote]

and for the Riesel problem he stated:
[quote]
We have a 50% chance of solving Riesel problem at N = 2^70 about 10^21.
We have a 5% chance of solving it at N = 2^47 about 10^14.
We have a 95% chance of solving it at N = 2^134 about 10^40.
Note also that the chances at 2^20, 2^25 and 2^30 are respectively about 10^-40, 10^-16 and 10^-8.
[/quote]

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

just an idea of time for only [b]one[/b] conjecture!

 MrOzzy 2008-10-16 10:06

I also found a better solution for Riesel base 66:

101954772 (was 144915105) with covering set:
67 for even n
7,17,37,73,613 for odd n.

In case I missed something, here are the primes considered: 67,4423,4357,7,613,17,409,2729,19,109,37,512713,37057,73,15217,14653,97,60289,937,1153

 robert44444uk 2008-10-16 10:28

I am happy to post the Sierpinski side but I need to organise my results, which are considering primes up to 100000 and up to 144-cover.

I can also check the work done on the Riesel side up to similar limits. i am using the revised covering.exe program so it will be interesting to see if I come up with alternative values! I will do this before doing the Sierpinski.

 Siemelink 2008-10-16 19:01

[QUOTE=MrOzzy;145536]I've found a better conjecture for Riesel base 71: 1132052528 in stead of 80375729488 like it is listed in the file you supplied.[/QUOTE]

That's quite possible, I didn't try to find the lowest riesel, only the riesel with the lowest amount of primes.

Willem.

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