Sierp base 3 reservations/statuses/primes - Page 5

gd_barnes · 2008-05-10, 07:45

Sierp base 3 now complete to k=15M and n=25K. Continuing on to k=30M.

In the range of, k=10M-15M, 16 more k's were found to be remaining in addition to the 4 k's that were effectively found by KEP on his k=110M-120M search for a total of 20.

This now leaves 56 k's remaining for k<15M and n=25K. The total k's remaining including the k=110M-120M range to n=25K is now 119.

All k's remaining are shown on the Sierp base 3 reservations page.

Gary

michaf · 2008-05-11, 07:48

My idea what an ideal program would do on base 3 conjecture:

1) upto the limit of remaining k's: just search for n=1 to 100, when a prime found, next k
2) Store all remaining k's in memory, and sieve from n=101 to 1000 to the optimum sievedepth. As a crude estimate it will take about 1k of memory per k, so on a 4G system we could fit in some 4M remaining k's
3) Primetest from 101 to 1000
By this time, a huge load is already eliminated, and the results which are left, can be written to disc, without storage problems.
4) if tested to n=1000, I guestimate that for each 1M candidates some 100 will remain, so for Riesel base 3, we will be left with 74M * 100 = 7,4G candidate k's

Which is still a huge load, but those can again be sieved in 4M batches to n=25k

Priority can be changed at all time from 100-1k and 1k-25k (and eventually 25k-100k etc...)

now... if someone has the capacity to program...

KEP · 2008-05-11, 08:29

Quote:

Originally Posted by michaf

My idea what an ideal program would do on base 3 conjecture:

1) upto the limit of remaining k's: just search for n=1 to 100, when a prime found, next k
2) Store all remaining k's in memory, and sieve from n=101 to 1000 to the optimum sievedepth. As a crude estimate it will take about 1k of memory per k, so on a 4G system we could fit in some 4M remaining k's
3) Primetest from 101 to 1000
By this time, a huge load is already eliminated, and the results which are left, can be written to disc, without storage problems.
4) if tested to n=1000, I guestimate that for each 1M candidates some 100 will remain, so for Riesel base 3, we will be left with 74M * 100 = 7,4G candidate k's

Which is still a huge load, but those can again be sieved in 4M batches to n=25k

Priority can be changed at all time from 100-1k and 1k-25k (and eventually 25k-100k etc...)

now... if someone has the capacity to program...

I like your ideas, it actually sounds a lot like what I was hoping to see someone cock together for us some day. Only thing we has to remember is, if such program ever gets programmed, it has to work in the command promt since that will give any BOINC projects e.g. Primegrid or RieselSieve an easy way to help us since thats according to Rytis and what he told me way back in time, it is easier to get programs working with boinc if they work in command line mode.

Now back to your idea, I actually think that attacking to 100, a range of e.g. 1 G k's would leave us about 100,000 k's according to your stats. It's a lot to sieve, but since they only has to be sieved from n 101-1000 optimal sievedepth would pretty fast be reached since testing time for Base 3 at n=<1,000 is very small. So actually I like these ideas, because I was told back in the future that it always is easier and faster to sieve millions or billions of pairs at same time in stead of just 1 k at a time. Now I suggest following to be done:

Sive remaining k/n pairs from n=<1,000 < n < 25,000. At n=25,000 for Riesel base 3 we would have only about 80M k's remaining. These should then be sieved to n=< 25,001 < n < 50,000. Calculations hasn't been done as to how many can be expected to be found for n between 25,001 to 50,000. And of course it can't be sieved all k's at once, especially not unless the k limit is going to be at 64 bits in stead fo 32 bits.

Hope I got it all, but maybe if someone choose to try to make such a program, we should suspend any work on the base 3, base 7, base 15 and maybe the remaining base 25 conjectures since we would waste a lot of time not needed to be wasted then. Also I think it would be more worthy to try to bring down the amount of unproven conjectures and then "if such program gets coded" launch a major and combined attack on that individually hard bases.

Just my thoughts.

Take care!

KEP

KEP · 2008-05-12, 10:48

A quick question, to whome ever feel quilified to answer it:

Why, if all odd k-values has trivial factors of 3 for any n for Base 3, both Sierpinski and Riesel, is k=1 not the lowest conjectured k? Just came to think about it, since I thought we were looking for the lowest k unable to ever raise a prime, so anyone has an explanation?

Regards

KEP!

gd_barnes · 2008-05-13, 18:24

Quote:

Originally Posted by KEP

A quick question, to whome ever feel quilified to answer it:

Why, if all odd k-values has trivial factors of 3 for any n for Base 3, both Sierpinski and Riesel, is k=1 not the lowest conjectured k? Just came to think about it, since I thought we were looking for the lowest k unable to ever raise a prime, so anyone has an explanation?

Regards

KEP!

KEP,

For base 3, odd k-values have a trivial factor of 2, not 3. And further: Any odd base odd k-values have a trivial factor of 2.

1*3^1+1 = 4; is not prime nor can any n-value be prime because they all give an answer that is divisible by 2.

1*3^1-1 = 2; is prime so cannot be the conjecture but is not considered for the same reason as the Sierp k=1.

And taking it one step further on the Sierp side, we don't consider Generallized Fermat numbers, i.e. numbers that can reduce to the form b^n+1, because for it to be prime, n must be a perfect square and so the # of possible primes is very limited and in many cases not possible to find with our current knowledge, even if one does exist. 1*3^n+1 would be a GFN.

You'll see a listing of GFN's without a prime on the right side of the main conjectures pages (if it doesn't have a trivial factor like base 3 does) but those are not considered as k's remaining.

Gary

KEP · 2008-05-13, 20:21

Quote:

Originally Posted by gd_barnes

KEP,

For base 3, odd k-values have a trivial factor of 2, not 3. And further: Any odd base odd k-values have a trivial factor of 2.

1*3^1+1 = 4; is not prime nor can any n-value be prime because they all give an answer that is divisible by 2.

1*3^1-1 = 2; is prime so cannot be the conjecture but is not considered for the same reason as the Sierp k=1.

And taking it one step further on the Sierp side, we don't consider Generallized Fermat numbers, i.e. numbers that can reduce to the form b^n+1, because for it to be prime, n must be a perfect square and so the # of possible primes is very limited and in many cases not possible to find with our current knowledge, even if one does exist. 1*3^n+1 would be a GFN.

You'll see a listing of GFN's without a prime on the right side of the main conjectures pages (if it doesn't have a trivial factor like base 3 does) but those are not considered as k's remaining.

Gary

Ah I see now

Now a status on my current work:

Base 19 sierpinski is at n=10444 and a total of 30 primes has been found and 22 made public for now.
Base 12 sierpinski is at n=119646 and a total of 531 tests has been conducted, no primes yet

Base 27 riesel. I'm actually considering releasing the 2 portions of sieved files aswell as the command-line.txt for rogue or other interested, since I'm in way over my head and really would like to focus fully on bringing down the sierpinski base 19 adn hopefully prove it, plus the time before I'm going to work further on the Base 27 Riesel range may be months in to the future, so I concluded that it would be most reasonable and fair to attach what work I've done on the range and release it to other more resourcesfull people.

So attached is following file:

Combo.zip which contains following files:

Base27_1.zip contains the first of 2 sieve portions for base 27 riesel.
Base27_2.zip contains the last of 2 sieve portions for base 27 riesel.

A total of around 15,530 candidates remain below n 1M.

Thanks and good luck to whoever takes this range and continues it.

Regards

KEP!

gd_barnes · 2008-05-19, 07:12

Quote:

Originally Posted by KEP

Ah I see now

Now a status on my current work:

Base 19 sierpinski is at n=10444 and a total of 30 primes has been found and 22 made public for now.
Base 12 sierpinski is at n=119646 and a total of 531 tests has been conducted, no primes yet

Base 27 riesel. I'm actually considering releasing the 2 portions of sieved files aswell as the command-line.txt for rogue or other interested, since I'm in way over my head and really would like to focus fully on bringing down the sierpinski base 19 adn hopefully prove it, plus the time before I'm going to work further on the Base 27 Riesel range may be months in to the future, so I concluded that it would be most reasonable and fair to attach what work I've done on the range and release it to other more resourcesfull people.

So attached is following file:

Combo.zip which contains following files:

Base27_1.zip contains the first of 2 sieve portions for base 27 riesel.
Base27_2.zip contains the last of 2 sieve portions for base 27 riesel.

A total of around 15,530 candidates remain below n 1M.

Thanks and good luck to whoever takes this range and continues it.

Regards

KEP!

KEP,

Thanks for releasing your sieved files here. One question: What ranges have you sieved?

It looks like in one file you've sieved fully to 5195043419339, i.e. 5.195T. In the other file, it shows 14140965245863, i.e. 14.141T but it has more k's remaining.

If you can clarify the ranges sieved, then we'll known what we need to sieve to complete the task.

Thanks,
Gary

gd_barnes · 2008-05-19, 08:58

Quote:

Originally Posted by michaf

I'll be trying out testing Sierp base 3 from k=100M to k=110M (upto n=25k)
(I've tested 100M to 100.01M, and it left zero candidates)

Micha,

Can you give us a status on this effort?

Thanks,
Gary

michaf · 2008-05-21, 10:10

100 to 110M is done, I have the files to my avail now, but am figuring out how to get the remaining numbers out easily :>

Quote:

Originally Posted by gd_barnes

Micha,

Can you give us a status on this effort?

Thanks,
Gary

michaf · 2008-05-21, 22:08

These are the sequences which have no primes upto 25k:

Code:

100143534*3^n+1
100190284*3^n+1
100193792*3^n+1
100670062*3^n+1
100852424*3^n+1
100999194*3^n+1
101186136*3^n+1
101311318*3^n+1
101315816*3^n+1
101349544*3^n+1
101619814*3^n+1
101818118*3^n+1
102014072*3^n+1
102046676*3^n+1
102127076*3^n+1
102159132*3^n+1
102281274*3^n+1
102531558*3^n+1
102746214*3^n+1
102857408*3^n+1
102862036*3^n+1
103152904*3^n+1
103267408*3^n+1
103270912*3^n+1
103321514*3^n+1
103323622*3^n+1
103396498*3^n+1
103950370*3^n+1
104168308*3^n+1
104618212*3^n+1
104882964*3^n+1
104927976*3^n+1
105070822*3^n+1
105080544*3^n+1
105207608*3^n+1
105492768*3^n+1
106047226*3^n+1
106065522*3^n+1
106148886*3^n+1
106337178*3^n+1
106349294*3^n+1
106430128*3^n+1
106463062*3^n+1
106634644*3^n+1
106646518*3^n+1
106743948*3^n+1
106967156*3^n+1
107217094*3^n+1
107248756*3^n+1
107463828*3^n+1
107468612*3^n+1
107617826*3^n+1
107778904*3^n+1
108009836*3^n+1
108143806*3^n+1
108232966*3^n+1
108326796*3^n+1
108410678*3^n+1
108520572*3^n+1
108532532*3^n+1
108609752*3^n+1
108638384*3^n+1
108776886*3^n+1
108790434*3^n+1
109042244*3^n+1
109116134*3^n+1
109384864*3^n+1
109486222*3^n+1
109668712*3^n+1
109832148*3^n+1
109842394*3^n+1
109908926*3^n+1

gd_barnes · 2008-05-23, 07:26

Quote:

Originally Posted by michaf

These are the sequences which have no primes upto 25k:

Code:

100143534*3^n+1
100190284*3^n+1
100193792*3^n+1
100670062*3^n+1
100852424*3^n+1
100999194*3^n+1
101186136*3^n+1
101311318*3^n+1
101315816*3^n+1
101349544*3^n+1
101619814*3^n+1
101818118*3^n+1
102014072*3^n+1
102046676*3^n+1
102127076*3^n+1
102159132*3^n+1
102281274*3^n+1
102531558*3^n+1
102746214*3^n+1
102857408*3^n+1
102862036*3^n+1
103152904*3^n+1
103267408*3^n+1
103270912*3^n+1
103321514*3^n+1
103323622*3^n+1
103396498*3^n+1
103950370*3^n+1
104168308*3^n+1
104618212*3^n+1
104882964*3^n+1
104927976*3^n+1
105070822*3^n+1
105080544*3^n+1
105207608*3^n+1
105492768*3^n+1
106047226*3^n+1
106065522*3^n+1
106148886*3^n+1
106337178*3^n+1
106349294*3^n+1
106430128*3^n+1
106463062*3^n+1
106634644*3^n+1
106646518*3^n+1
106743948*3^n+1
106967156*3^n+1
107217094*3^n+1
107248756*3^n+1
107463828*3^n+1
107468612*3^n+1
107617826*3^n+1
107778904*3^n+1
108009836*3^n+1
108143806*3^n+1
108232966*3^n+1
108326796*3^n+1
108410678*3^n+1
108520572*3^n+1
108532532*3^n+1
108609752*3^n+1
108638384*3^n+1
108776886*3^n+1
108790434*3^n+1
109042244*3^n+1
109116134*3^n+1
109384864*3^n+1
109486222*3^n+1
109668712*3^n+1
109832148*3^n+1
109842394*3^n+1
109908926*3^n+1

The following 9 k's reduce to k-values already found with no known primes to n=25K and hence are not considered remaining:

Code:

k-value     reduces to
101186136   11242904
102281274   11364586
102746214   11416246
104927976   11658664
105080544    3891872
106065522   11785058
106337178    3938414
108790434   12087826
109832148   12203572

The following 11 k's reduce to k-values that have not yet been searched and have no prime at n=1, and hence will be shown at their reduced values:

Code:

k-value     reduces to
100143534   33381178
100999194   33666398
102531558   34177186
104882964   34960988
105492768   35164256
106148886   35382962
106743948   35581316
107463828   35821276
108326796   36108932
108520572   36173524
108776886   36258962

The remaining 52 k-values will be shown as is and remaining for k=100M-110M to n=25K. This includes k=102159132, which can reduce to k=34053044 but has a prime at n=1, hence is the only k-value considered remaining in the range that is divisible by 3.

Gary

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2008-05-10, 07:45	#45
gd_barnes "Gary" May 2007 Overland Park, KS 5·7·359 Posts	Sierp base 3 now complete to k=15M and n=25K. Continuing on to k=30M. In the range of, k=10M-15M, 16 more k's were found to be remaining in addition to the 4 k's that were effectively found by KEP on his k=110M-120M search for a total of 20. This now leaves 56 k's remaining for k<15M and n=25K. The total k's remaining including the k=110M-120M range to n=25K is now 119. All k's remaining are shown on the Sierp base 3 reservations page. Gary

2008-05-11, 07:48	#46
michaf Jan 2005 479 Posts	My idea what an ideal program would do on base 3 conjecture: 1) upto the limit of remaining k's: just search for n=1 to 100, when a prime found, next k 2) Store all remaining k's in memory, and sieve from n=101 to 1000 to the optimum sievedepth. As a crude estimate it will take about 1k of memory per k, so on a 4G system we could fit in some 4M remaining k's 3) Primetest from 101 to 1000 By this time, a huge load is already eliminated, and the results which are left, can be written to disc, without storage problems. 4) if tested to n=1000, I guestimate that for each 1M candidates some 100 will remain, so for Riesel base 3, we will be left with 74M * 100 = 7,4G candidate k's Which is still a huge load, but those can again be sieved in 4M batches to n=25k Priority can be changed at all time from 100-1k and 1k-25k (and eventually 25k-100k etc...) now... if someone has the capacity to program...

2008-05-12, 10:48	#48
KEP Quasi Admin Thing May 2005 2×5×101 Posts	A quick question, to whome ever feel quilified to answer it: Why, if all odd k-values has trivial factors of 3 for any n for Base 3, both Sierpinski and Riesel, is k=1 not the lowest conjectured k? Just came to think about it, since I thought we were looking for the lowest k unable to ever raise a prime, so anyone has an explanation? Regards KEP!