Twin prime search? - Page 8

MooMoo2 · 2006-05-28, 19:36

Quote:

Originally Posted by pacionet

Also on my Pentium 4, 3.2 Ghz testing -1 k's is faster:

186002877*2^195000-1 is prime! Time : 104.031 sec.
186002877*2^195000+1 is not prime. Proth RES64: 29FD50C0848E4FEE Time: 104.398 sec.

Congrats! That's the 20th prime we found!

pacionet · 2006-06-20, 13:53

Updated stats on our site:

www.twinprimesearch.org

If I didn't any errors (sorry but for the moment site pages and stats are still manually updated):

John Renze is the best tester for MILLIONS TESTED
lsoule is the best tester for PRIMES FOUND

Congrats, guys !

Jean Penné · 2006-06-20, 14:48

Hi,
I am slightly wondering about your choice of testing only odd k's while
testing with a fixed n...
Indeed, on may always say that 2*u*2^195000-1 is u*2^195001-1, but
the problem is that k*2^195000-1 and (k+1)*2^195000-1 are almost of
the same size...
And Newpgen can do that without any lose in the performance.
Would you excuse my remark from a non participant (but very interested) guy!

I think also that you know about of the last success of the Hungarian team...
But I am sure that, at last, David will beat Goliath, as it happened with GIMPS!

With my best wishes of good luck,
Jean

MooMoo2 · 2006-06-20, 19:54

Quote:

Originally Posted by Jean Penné

Hi,
I am slightly wondering about your choice of testing only odd k's while
testing with a fixed n...
Indeed, on may always say that 2*u*2^195000-1 is u*2^195001-1, but
the problem is that k*2^195000-1 and (k+1)*2^195000-1 are almost of
the same size...
And Newpgen can do that without any lose in the performance.
Would you excuse my remark from a non participant (but very interested) guy!

I think also that you know about of the last success of the Hungarian team...
But I am sure that, at last, David will beat Goliath, as it happened with GIMPS!

With my best wishes of good luck,
Jean

The reason is what you've previously mentioned: A prime of, say, 2002*2^195000-1 is actually 1001*2^195001-1. This may be nothing more than a minor issue now, but it will lead to confusion if we do decide (later) to test for primes of k*2^195001-1. I'm definitely not planning to move to another n any time soon, but there is a small chance that the situation may change.

Also, there are plenty of odd k's to test, and a k around 20M takes the same time to test as a k around 200M. So even if we decided to test even k's, there would not be a speed improvement.

P.S. I think the Hungarian team's last success is discovering the largest Sophie Germain prime

http://primes.utm.edu/top20/page.php?id=2

---------------------------------------------------------------
pacionet,

I think that on your home page, you should include these as news items:

- We've tested over 250M of ranges
- We've found over 50 primes

Of course, the news item we all want to see is:

- Member ??? has found a twin prime! Congrats on the world record!

R. Gerbicz · 2006-06-20, 20:50

Quote:

Originally Posted by MooooMoo

T
P.S. I think the Hungarian team's last success is discovering the largest Sophie Germain prime

And don't forget about Papp Dániel, he is also Hungarian and he hold the twin prime record for three years by 33218925*2^169690+-1 by a big luck, see his bio at: http://primes.utm.edu/bios/page.php?id=373

pacionet · 2006-06-20, 21:06

Sophie-Germaine ?
Maybe in the future I'll organize a "Sophie-Germain Internet Prime Search"

, but first focus on twin primes and try to find the largest one.

paulunderwood · 2006-06-20, 22:55

Quote:

P.S. I think the Hungarian team's last success is discovering the largest Sophie Germain prime

http://primes.utm.edu/top20/page.php?id=2

The've just beat their own recent twin prime record:

http://primes.utm.edu/primes/page.php?id=77996
http://primes.utm.edu/primes/page.php?id=77997

topping:

http://primes.utm.edu/top20/page.php?id=1

smh · 2006-06-20, 23:08

Quote:

So even if we decided to test even k's, there would not be a speed improvement.

There will be. You are actually sieveing twice as many candidates in about the same time, so you could have choosen a range half the size. Doesn't make a whole lot of diffenence though.

pacionet · 2006-06-21, 07:40

Quote:

Originally Posted by paulunderwood

The've just beat their own recent twin prime record:

http://primes.utm.edu/primes/page.php?id=77996
http://primes.utm.edu/primes/page.php?id=77997

topping:

http://primes.utm.edu/top20/page.php?id=1

Yes they set a new world record in these days. Anyway our exponent is still greater than theirs, so we can go on in our search.

I like this challenge !

2006-06-22, 07:45

Quote:

Originally Posted by MooooMoo

...but it will lead to confusion if we do decide (later) to test for primes of k*2^195001-1. I'm definitely not planning to move to another n any time soon, but there is a small chance that the situation may change.

Yeah, but one would not change to an nn just 1 greater. That's lame

Make it at least a few hundred more.

Kosmaj · 2006-06-22, 07:49

Hello! Just a few observations from yet another silent observer of your interesting project.
(1) I think your choice of n is a bit too high, in your place I'd select n close to 175k because even at that level the task is very hard.
(2) I second the opinion that omitting even k's was not the best idea. If you process all even and odd k<k1 at n=195000, than when you switch to n=195001 all you have to do is start sieving from k=k1/2.
(3) I'd like to suggest more sieving. For exact limit you can compare LLR exe time with the time needed to seive out a single candidate. My rough estimation is 250-300T at least. You can organize distributed sieving using NewPGen.

It's too late for 1-2, but you can try (3).

Finally, I wish you best of luck!

ps. Jarai et al. beat their own twin record for just one digit as they appearantly kept on working on the same exponent n=171960 like the one in their old twin record and in the new Sophie Germain record. Which means they are doing a variation of the so-called "lucky minus". Although their k in the record twin is huge they don't check all k's but only those divisible by 5*7*11 and maybe not even all of those. BTW, Jarai was a member of the famous trio Indlekofer, Jarai, Wassing who found many twin and Sophie Germain primes in 1990's... Details can be found on the Top-5000 web site.

2006-06-20, 14:48	#80
Jean Penné May 2004 FRANCE 2⁴·3·13 Posts	Why are you testing only odd k's ? Hi, I am slightly wondering about your choice of testing only odd k's while testing with a fixed n... Indeed, on may always say that 2u2^195000-1 is u2^195001-1, but the problem is that k2^195000-1 and (k+1)*2^195000-1 are almost of the same size... And Newpgen can do that without any lose in the performance. Would you excuse my remark from a non participant (but very interested) guy! I think also that you know about of the last success of the Hungarian team... But I am sure that, at last, David will beat Goliath, as it happened with GIMPS! With my best wishes of good luck, Jean

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2006-06-20, 13:53	#79
pacionet Oct 2005 Italy 3×113 Posts	Updated stats on our site: www.twinprimesearch.org If I didn't any errors (sorry but for the moment site pages and stats are still manually updated): John Renze is the best tester for MILLIONS TESTED lsoule is the best tester for PRIMES FOUND Congrats, guys !

2006-06-20, 21:06	#83
pacionet Oct 2005 Italy 523₈ Posts	Sophie-Germaine ? Maybe in the future I'll organize a "Sophie-Germain Internet Prime Search" , but first focus on twin primes and try to find the largest one.

2006-06-22, 07:49	#88
Kosmaj Nov 2003 2×1,811 Posts	Hello! Just a few observations from yet another silent observer of your interesting project. (1) I think your choice of n is a bit too high, in your place I'd select n close to 175k because even at that level the task is very hard. (2) I second the opinion that omitting even k's was not the best idea. If you process all even and odd k<k1 at n=195000, than when you switch to n=195001 all you have to do is start sieving from k=k1/2. (3) I'd like to suggest more sieving. For exact limit you can compare LLR exe time with the time needed to seive out a single candidate. My rough estimation is 250-300T at least. You can organize distributed sieving using NewPGen. It's too late for 1-2, but you can try (3). Finally, I wish you best of luck! ps. Jarai et al. beat their own twin record for just one digit as they appearantly kept on working on the same exponent n=171960 like the one in their old twin record and in the new Sophie Germain record. Which means they are doing a variation of the so-called "lucky minus". Although their k in the record twin is huge they don't check all k's but only those divisible by 5711 and maybe not even all of those. BTW, Jarai was a member of the famous trio Indlekofer, Jarai, Wassing who found many twin and Sophie Germain primes in 1990's... Details can be found on the Top-5000 web site.