Smarandache prime(s) - Page 6

wombatman · 2015-10-14, 19:53

Alrighty then. Guess I can stop my run

LaurV · 2015-10-15, 10:38

Quote:

Originally Posted by Batalov

(and in parallel am sieving up to 10^11 for 140000<n<200000)

Just to make it clear: you have ~1100 candidates remaining between 10^5 and 10^6-1 ?

Batalov · 2015-10-15, 16:43

No of course between 100k and 200k.
Only a madman would go above 200k; I am not mad enough!

Because the sieve is not a baby-step giant-step sieve (we can't take the logmod), its speed depends on length of the interval (more directly - on number of survivors), so I am sieving only those that I can run. The tests at 155k take already 7-8 hours.

LaurV · 2015-10-16, 01:44

:phew: ! (where is the icon with the guy wiping his forehead?)
You took the stone out from my heart. Now we are good.
I was wondering how the hack I could be so wrong in my estimation. As you could see from my posts and code, I was always talking about 0 to 10^6-1 (not from 10^5, but from 0).

(of course I understand that you still reduced my estimation to almost half, and of course this post does not take back anything I said in post #54 about you and R. Gerbicz)

Batalov · 2015-10-17, 17:57

Here is the sieve file for values 200k-1M, lightly sieved to 1G (of course in this range it needs at least 1T, which I am in process of doing for 200-300k which I may foolishly do next).

Because my sieve cannot use primes 11, 37, 41, 101, 271 (it has divmod) and because it needs more modding if p are small, the initial pre-sieve is done with this easy script:

Code:

#! gp
P=7;forprime(p=11,100000,P*=p);
x=Mod(123456789,P);m=100;for(i=10,200000,if(i>=m,m*=10);x=x*m+i)
for(n=200001,1000000,x=x*m+n;if(n%6==1 && n%5>0 && gcd(lift(x),P)==1,write("Input200k_c",n)))

Batalov · 2015-10-17, 20:08

In near future, I will start a PRPNet server 'The Great Smarandache PRP search'.
Then we can reach the million and find the expected 0.6 primes.

Expect very long run times (days). Stable *Bridges/*wells will do well in this project.
I will sieve to the needed depth and take care of the server (some trivial code modifications will be taken care of, too).

ewmayer · 2015-10-17, 21:19

Quote:

Originally Posted by Batalov

In near future, I will start a PRPNet server 'The Great Smarandache PRP search'.
Then we can reach the million and find the expected 0.6 primes.

See my update to the estimate thread - your odds are now above 1! Of course those are the naive odds - the conditional odds given no primes found below 10^5 are still quite low for the 10^5 - 10^6 range, around 10%. Now I know what you're thinking - did he do 6 log10s or just 5? Well to be honest, in all that excitement I kinda lost count myself, &c ... Do you feel lucky, punk?

Batalov · 2015-10-18, 00:41

Ok, pssst...
The secret phrase is ~~squamous ossifrage~~

Code:

//============= in prpclient.ini =============
//   <suffix>:<pct>:<workunits>:<server IP>:<port>
server=SmarPRP:100:1:99.121.249.54:1200

That goes in your prpclient.ini and you should have your pfgwexe set.
The Windows 64-bit prpclient binary is attached for those who don't have it. Or get it from here.

The current status is here: http://99.121.249.54:1200/

The credit for the find will go to "A,B,PFGW", where A is the finder, B is me and PFGW is Mark+George and other authors of PFGW.

Batalov · 2015-10-18, 16:59

P.S. The server is now debugged and is working fine; two candidates were already processed by my little laptop, turned in and marked.
Removal of candidates (above 260k) by the on-going sieving (on 36 EC2 cores) works great, too. Kudos to Mark!

Everyone is welcome to attach to PRPNet server and make history! I'll copy the PRPNet post to the top post, too.

rogue · 2015-10-18, 17:24

What is the speed of the sieve on a single core? The OpenCL factorial sieving code could be extended for this form. Instead of multiplying by n in each iteration, multiply by 1, 10, 100, etc. then after the mulmod add n. and do one last subtraction of p (if necessary).

Batalov · 2015-10-18, 17:40

I'll compare the sieves.

The sieve that I am using is a few posts above -- it is not GPU-assisted but it does leap forward in n space by 90-100 for each candidate while a naive sieve will do 90-100 modmuls for the same step.
For each p, it also directly starts from n₀ (e.g. 200113) while the naive sieve will go for 200000 modmuls just to prepare the first value.

2015-10-17, 20:08	#61
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 2516₁₆ Posts	PRPNet server 'The Great Smarandache PRP search' pre-announcement In near future, I will start a PRPNet server 'The Great Smarandache PRP search'. Then we can reach the million and find the expected 0.6 primes. Expect very long run times (days). Stable Bridges/wells will do well in this project. I will sieve to the needed depth and take care of the server (some trivial code modifications will be taken care of, too).

2015-10-18, 17:24	#65
rogue "Mark" Apr 2003 Between here and the 2×3²×353 Posts	What is the speed of the sieve on a single core? The OpenCL factorial sieving code could be extended for this form. Instead of multiplying by n in each iteration, multiply by 1, 10, 100, etc. then after the mulmod add n. and do one last subtraction of p (if necessary). Last fiddled with by rogue on 2020-09-24 at 19:47

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2015-10-14, 19:53	#56
wombatman I moo ablest echo power! May 2013 13×137 Posts	Alrighty then. Guess I can stop my run

2015-10-15, 16:43	#58
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 22426₈ Posts	No of course between 100k and 200k. Only a madman would go above 200k; I am not mad enough! Because the sieve is not a baby-step giant-step sieve (we can't take the logmod), its speed depends on length of the interval (more directly - on number of survivors), so I am sieving only those that I can run. The tests at 155k take already 7-8 hours.

2015-10-16, 01:44	#59
LaurV Romulan Interpreter Jun 2011 Thailand 25B9₁₆ Posts	:phew: ! (where is the icon with the guy wiping his forehead?) You took the stone out from my heart. Now we are good. I was wondering how the hack I could be so wrong in my estimation. As you could see from my posts and code, I was always talking about 0 to 10^6-1 (not from 10^5, but from 0). (of course I understand that you still reduced my estimation to almost half, and of course this post does not take back anything I said in post #54 about you and R. Gerbicz)

2015-10-18, 16:59	#64
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 9494₁₀ Posts	P.S. The server is now debugged and is working fine; two candidates were already processed by my little laptop, turned in and marked. Removal of candidates (above 260k) by the on-going sieving (on 36 EC2 cores) works great, too. Kudos to Mark! Everyone is welcome to attach to PRPNet server and make history! I'll copy the PRPNet post to the top post, too.

2015-10-18, 17:40	#66
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 2·47·101 Posts	I'll compare the sieves. The sieve that I am using is a few posts above -- it is not GPU-assisted but it does leap forward in n space by 90-100 for each candidate while a naive sieve will do 90-100 modmuls for the same step. For each p, it also directly starts from n₀ (e.g. 200113) while the naive sieve will go for 200000 modmuls just to prepare the first value.