Sierp base 3 reservations/statuses/primes - Page 7

michaf · 2008-05-30, 18:38

Quote:

Originally Posted by michaf

Sr2sieve started to make the legendre tables, and quitted at about 60% done. Is there a way to NOT make the tables?

And no, I haven't used -t as starters, but will check all the primes later on indeed.

I just done the checking... it get's to about 500 per second on average (measured on sight). So it's done rather quickly.

KEP · 2008-05-30, 19:45

@Michaf and maybe Gary:

I remember in some of the either srsieve.exe, sr1sieve.exe or sr2sieve.exe, that using the -X or -x will force either srsieve.exe, sr1sieve.exe or sr2sieve.exe or all of the mentioned programs, to start sieving without the use of Even- and odd legendre tables. I'm not sure if I remember right.

Also Michaf, you should be using -t for your sierpinski testing, that way you're sure that your NOprimes.out list is only containing those that for 100% curtanty is not a prime k for the given nmax. That way you can start sieveing emediately on the reamining k's up to nmax (25,000) -1. You have to sieve to nmax-1 and then once optimal sieve depth is reached, using srsieve you have to copy all remaining k's from the "NOprimes.out" file, in which you replace "*3^n+1" with " 25000", to the presieved file. When that is done you have to change the first line in the presieved NewPGen file to "ABC $a*3^$b+1 // {number_primes,$a,1}" to make sure that no k's is tested more than once if a prime is found. By copying the remaining k's list into the presieved NewPGen file, you just has to make a log file in which you saves the remaining k's there were tested at n=25,000. That way you rather easy has the remaining k's without to much of a hassel

Hope this made sence

else feel free to ask again...

KEP!

gd_barnes · 2008-05-31, 05:31

Quote:

Originally Posted by KEP

@Michaf and maybe Gary:

I remember in some of the either srsieve.exe, sr1sieve.exe or sr2sieve.exe, that using the -X or -x will force either srsieve.exe, sr1sieve.exe or sr2sieve.exe or all of the mentioned programs, to start sieving without the use of Even- and odd legendre tables. I'm not sure if I remember right.

Also Michaf, you should be using -t for your sierpinski testing, that way you're sure that your NOprimes.out list is only containing those that for 100% curtanty is not a prime k for the given nmax. That way you can start sieveing emediately on the reamining k's up to nmax (25,000) -1. You have to sieve to nmax-1 and then once optimal sieve depth is reached, using srsieve you have to copy all remaining k's from the "NOprimes.out" file, in which you replace "*3^n+1" with " 25000", to the presieved file. When that is done you have to change the first line in the presieved NewPGen file to "ABC $a*3^$b+1 // {number_primes,$a,1}" to make sure that no k's is tested more than once if a prime is found. By copying the remaining k's list into the presieved NewPGen file, you just has to make a log file in which you saves the remaining k's there were tested at n=25,000. That way you rather easy has the remaining k's without to much of a hassel

Hope this made sence

else feel free to ask again...

KEP!

It's generally must faster to NOT use the -t option and then prove all primes after it is through searching all k-values. It's EXTREMELY rare that a PRP is not a prime...so rare that it happens less frequently than your computer having a memory (or other) error that causes a prime to be missed or a prime to be found that is not one.

If you happen to find one that is not a prime, it's easy enough to re-test that k-value for primes at higher n-values. Even in 100M k-values, it's highly unlikely that any PRP is not prime.

If I used the -t option in PFGW for testing to n=25K, it would take a ridiculous amount of time.

Gary

michaf · 2008-06-02, 17:16

Gary, here are the leftovers from 30-50M sierpinski, I haven't checked for the ones divisible by 3

118 remaining:

Code:

Just checked: results are:

Code:

30672498	0	10224166	IS already being tested
31513908	0	10504636	IS already being tested
33728712	0	11242904	IS already being tested
34093758	0	11364586	IS already being tested
34248738	0	11416246	IS already being tested
34975992	0	11658664	IS already being tested
35355174	0	11785058	IS already being tested
36263478	0	12087826	IS already being tested
36610716	0	12203572	IS already being tested
37687218	0	12562406	IS already being tested
37991706	0	12663902	IS already being tested
39563346	0	13187782	IS already being tested
39940302	0	13313434	IS already being tested
40872108	0	13624036	IS already being tested
41362008	0	13787336	IS already being tested
42415944	0	14138648	IS already being tested
43363668	0	14454556	IS already being tested
44676948	0	14892316	IS already being tested
44766102	0	14922034	IS already being tested
44982318	0	14994106	IS already being tested
45217878	0	15072626	IS already being tested
46190286	0	15396762	IS already being tested
47685468	0	15895156	IS already being tested
48758826	0	16252942	IS already being tested
48911568	0	16303856	IS already being tested
49057194	0	16352398	IS already being tested
49759116	0	16586372	IS already being tested
31881438	0	10627146	not in list --> keep it
32450112	0	10816704	not in list --> keep it
33040752	0	11013584	not in list --> keep it
35026848	0	11675616	not in list --> keep it
35445726	0	11815242	not in list --> keep it
37018368	0	12339456	not in list --> keep it
37158138	0	12386046	not in list --> keep it
38460564	0	12820188	not in list --> keep it
39301578	0	13100526	not in list --> keep it
41814252	0	13938084	not in list --> keep it
41941962	0	13980654	not in list --> keep it
43458984	0	14486328	not in list --> keep it
44770374	0	14923458	not in list --> keep it
46293816	0	15431272	not in list --> keep it
48746988	0	16248996	not in list --> keep it

so 27 already being tested --L> 118-27 = 91 remaining:

Code:

michaf · 2008-06-02, 17:46

Quote:

Originally Posted by gd_barnes

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

Gary

Which now means that these can all be removed, all are remaining as the reduces ones in the search

michaf · 2008-06-02, 18:54

I'm reserving 50-100M upto 25k, so no further gaps will be present

michaf · 2008-06-06, 10:00

Quote:

Originally Posted by michaf

I'm reserving 50-100M upto 25k, so no further gaps will be present

In case I was unclear: on Sierpinski-side.

gd_barnes · 2008-06-06, 19:26

Quote:

Originally Posted by michaf

Gary, here are the leftovers from 30-50M sierpinski, I haven't checked for the ones divisible by 3

118 remaining:

Code:

Just checked: results are:

Code:

30672498    0    10224166    IS already being tested
31513908    0    10504636    IS already being tested
33728712    0    11242904    IS already being tested
34093758    0    11364586    IS already being tested
34248738    0    11416246    IS already being tested
34975992    0    11658664    IS already being tested
35355174    0    11785058    IS already being tested
36263478    0    12087826    IS already being tested
36610716    0    12203572    IS already being tested
37687218    0    12562406    IS already being tested
37991706    0    12663902    IS already being tested
39563346    0    13187782    IS already being tested
39940302    0    13313434    IS already being tested
40872108    0    13624036    IS already being tested
41362008    0    13787336    IS already being tested
42415944    0    14138648    IS already being tested
43363668    0    14454556    IS already being tested
44676948    0    14892316    IS already being tested
44766102    0    14922034    IS already being tested
44982318    0    14994106    IS already being tested
45217878    0    15072626    IS already being tested
46190286    0    15396762    IS already being tested
47685468    0    15895156    IS already being tested
48758826    0    16252942    IS already being tested
48911568    0    16303856    IS already being tested
49057194    0    16352398    IS already being tested
49759116    0    16586372    IS already being tested
31881438    0    10627146    not in list --> keep it
32450112    0    10816704    not in list --> keep it
33040752    0    11013584    not in list --> keep it
35026848    0    11675616    not in list --> keep it
35445726    0    11815242    not in list --> keep it
37018368    0    12339456    not in list --> keep it
37158138    0    12386046    not in list --> keep it
38460564    0    12820188    not in list --> keep it
39301578    0    13100526    not in list --> keep it
41814252    0    13938084    not in list --> keep it
41941962    0    13980654    not in list --> keep it
43458984    0    14486328    not in list --> keep it
44770374    0    14923458    not in list --> keep it
46293816    0    15431272    not in list --> keep it
48746988    0    16248996    not in list --> keep it

so 27 already being tested --L> 118-27 = 91 remaining:

Code:

There is one thing that you're forgetting here Micha: You have to do more than just divide by 3. You have to divide by 3^q for all q>=1 until you reduce each k-value as far as possible. I don't have time to do this for all of your k-values but here's the first one that I found that can additionally be eliminated:

k=35026848 is divisible by 3^2 and hence reduces to k=3891872. k=3891872 is remaining so k=35026848 can be eliminated. You'll need to check the rest of them.

The first 3 k's in your list shown as 'not in list - keep it' should be kept. They reduce to k-values that are not remaining and they are not remaining because they have small primes for n<=4.

I know this seems like an administrative hassle at the low n-ranges in making sure that we get all of this filtered out but it will saves us a ton of CPU-time in the future.

Gary

michaf · 2008-06-06, 20:38

Quote:

Originally Posted by gd_barnes

There is one thing that you're forgetting here Micha: You have to do more than just divide by 3. You have to divide by 3^q for all q>=1 until you reduce each k-value as far as possible. I don't have time to do this for all of your k-values but here's the first one that I found that can additionally be eliminated:

k=35026848 is divisible by 3^2 and hence reduces to k=3891872. k=3891872 is remaining so k=35026848 can be eliminated. You'll need to check the rest of them.

Oh darn... I knew I should have, I had plainly forgotten... will do now..

Quote:

The first 3 k's in your list shown as 'not in list - keep it' should be kept. They reduce to k-values that are not remaining and they are not remaining because they have small primes for n<=4.

hence: keep it

Quote:

I know this seems like an administrative hassle at the low n-ranges in making sure that we get all of this filtered out but it will saves us a ton of CPU-time in the future.

Gary

No problem... better think now, then having to do it for a whole load later on...

michaf · 2008-06-06, 20:49

Results from rechecking:

the following k's can be removed, as they are already tested as their reduced forms: (div 3^2)

Code:

35026848	0	11675616	0	3891872	Is already being tested - remove from list	
35445726	0	11815242	0	3938414	Is already being tested - remove from list	
38460564	0	12820188	0	4273396	Is already being tested - remove from list	
41941962	0	13980654	0	4660218	Is already being tested - remove from list

The following can all be divided by 3^3, but are all smaller than the 2930054 lower limit of the smallest under test, so all need to be tested still:

Code:

31881438	0	10627146	0	3542382	0	1180794
32450112	0	10816704	0	3605568	0	1201856
39301578	0	13100526	0	4366842	0	1455614
41814252	0	13938084	0	4646028	0	1548676
43458984	0	14486328	0	4828776	0	1609592
44770374	0	14923458	0	4974486	0	1658162
48746988	0	16248996	0	5416332	0	1805444

The following is then the resulting k's that need to be tested between 30M and 50M (91-4= 87 of them)

Code:

and again, sorry for forgetting them, and thanks for reminding me.

(range 50-100M is now at 80M (to 10k))

gd_barnes · 2008-06-14, 21:12

Quote:

Originally Posted by michaf

Results from rechecking:

the following k's can be removed, as they are already tested as their reduced forms: (div 3^2)

Code:

35026848    0    11675616    0    3891872    Is already being tested - remove from list    
35445726    0    11815242    0    3938414    Is already being tested - remove from list    
38460564    0    12820188    0    4273396    Is already being tested - remove from list    
41941962    0    13980654    0    4660218    Is already being tested - remove from list

The following can all be divided by 3^3, but are all smaller than the 2930054 lower limit of the smallest under test, so all need to be tested still:

Code:

31881438    0    10627146    0    3542382    0    1180794
32450112    0    10816704    0    3605568    0    1201856
39301578    0    13100526    0    4366842    0    1455614
41814252    0    13938084    0    4646028    0    1548676
43458984    0    14486328    0    4828776    0    1609592
44770374    0    14923458    0    4974486    0    1658162
48746988    0    16248996    0    5416332    0    1805444

The following is then the resulting k's that need to be tested between 30M and 50M (91-4= 87 of them)

Code:

and again, sorry for forgetting them, and thanks for reminding me.

(range 50-100M is now at 80M (to 10k))

This is far short of straight-forward Micha. All except 2 of the k-values that you listed that are divisible by 3^3 CAN be eliminated!! Here's why: They reduce to k-values with LARGE primes as opposed to small primes.

Here's the rule on k's that reduce to k's that are no longer remaining:
1. If the reduced k has a large prime, then the larger k has the same large prime and can be eliminated.
2. If the reduced k has a small prime (usually n=1, but can be n=2 for k/3^2, n=3 for k/3^3, etc.), than the larger k remains.

In your case:
k=31881438 that reduces to k=1180794: k=1180794 has a prime only at n=3 so k=31881438 remains. (i.e. k=31881438 has a prime at n=0, but n must be >=1 hence k remains)
k=32450112 that reduces to k=1201856: k=1201856 has a prime only at n=3 so k=32450112 remains.
k=39301578 that reduces to k=1455614: k=1455614 has a prime at n=33885 so k=39301578 is eliminated.
k=41814252 that reduces to k=1548676: k=1548676 has a prime at n=103787 so k=41814252 is eliminated.
k=43458984 that reduces to k=1609592: k=1609592 has a prime at n=87201 so k=43458984 is eliminated.
k=44770374 that reduces to k=1658162: k=1658162 has a prime at n=32753 so k=44770374 is eliminated.
k=48746988 that reduces to k=1805444: k=1805444 has a prime at n=156750 so k=48746988 is eliminated.

More specifically, you have to look at each k individually that is divisible by a power of 3.

I could put together a detailed set of instructions for about every possible scenario but I just don't have the time to put it together right now.

I'll hold off on updating the k's remaining for k=30M-50M on the web pages until I have a chance to check things a little more.

Gary

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2008-05-30, 19:45	#68
KEP Quasi Admin Thing May 2005 2·3·7·23 Posts	@Michaf and maybe Gary: I remember in some of the either srsieve.exe, sr1sieve.exe or sr2sieve.exe, that using the -X or -x will force either srsieve.exe, sr1sieve.exe or sr2sieve.exe or all of the mentioned programs, to start sieving without the use of Even- and odd legendre tables. I'm not sure if I remember right. Also Michaf, you should be using -t for your sierpinski testing, that way you're sure that your NOprimes.out list is only containing those that for 100% curtanty is not a prime k for the given nmax. That way you can start sieveing emediately on the reamining k's up to nmax (25,000) -1. You have to sieve to nmax-1 and then once optimal sieve depth is reached, using srsieve you have to copy all remaining k's from the "NOprimes.out" file, in which you replace "3^n+1" with " 25000", to the presieved file. When that is done you have to change the first line in the presieved NewPGen file to "ABC $a3^$b+1 // {number_primes,$a,1}" to make sure that no k's is tested more than once if a prime is found. By copying the remaining k's list into the presieved NewPGen file, you just has to make a log file in which you saves the remaining k's there were tested at n=25,000. That way you rather easy has the remaining k's without to much of a hassel Hope this made sence else feel free to ask again... KEP!

2008-06-02, 18:54	#72
michaf Jan 2005 479 Posts	I'm reserving 50-100M upto 25k, so no further gaps will be present