General information about this project

Oddball · 2011-02-14, 01:30

Welcome! The Twin Prime Search (TPS) is, as you may have guessed, a project that looks for large twin primes. There are two efforts underway, which are described below.

Main subproject: We're mainly focused on a variable-n search for twins that are 144,000 - 151,000 digits long. There are two ways to participate - one is sieving, and the other is LLR testing. A quick and easy to remember analogy is that sieving acts as a shotgun and LLR testing acts as a sniper rifle when it comes to removing k/n pairs.

Sieving: This is a process that eliminates candidates by checking whether any of them have factors within a certain range. You will not find a twin or a prime by sieving, but choosing sieving over primality testing is often more effective in the long run. That's because you'll usually eliminate more candidates by sieving for a given period (1 day, for example) than by LLRing for the same amount of time. For TPS, sieving is best done by 64-bit computers that have at least 1GB of RAM, and you can visit this thread for further details on getting started with sieving: http://www.mersenneforum.org/showthread.php?t=12260

LLR testing: Most of the excitement and action happens here, as this is the only way to find primes and twins. LLR is a program that tests k/n pairs for primality one by one, and each candidate takes about 5 minutes to test on a single core PC. LLR testing can be done manually or automatically. Manual testing works similarly to sieving and is better suited for computers with very slow, nonexistent, or irregular internet access. More details on manual LLR reservations are here: http://www.mersenneforum.org/showthread.php?t=13387, and more details on automatic LLRing (which uses LLRnet and/or PRPnet) are here: http://www.mersenneforum.org/showthread.php?t=13805

Secondary subproject: Called "Operation Megabit Twin", this subproject searches for twins and Sophie Germain primes that are over a million binary digits long. LLR testing has not yet begun, but you can contribute to the sieve effort by heading over to http://www.mersenneforum.org/showthread.php?t=13439 and reserving a range.

So if you're hoping to get a world record, want to put your computer to good use, or are simply interested in math, why not take the next step and join us?

Oddball · 2011-02-14, 01:32

Historical Milestones:
April 13, 2006: Project founded, n=195000 effort started
Mid-November 2006: Collaboration with Primegrid starts
Mid-December 2006: Sieving of n=333333 begins
January 15, 2007: 2003663613*2^195000+/-1 twin found (58711 digits)
August 6, 2009: 65516468355*2^333333+/-1 twin found (100355 digits)
August 8, 2009: Start of variable-n search
May 10, 2010: Variable-n search resumed after months of inactivity
May 25, 2010: "Operation Megabit Twin" subproject begins
August 30, 2010: LLRnet and PRPNet servers introduced for the variable-n search
January 14-16, 2011: First TPS rally
March 29, 2011: Optimal sieve depth for n=480K-485K reached

Countdowns and odds (last updated 4/2/2011):
Countdown to reaching the optimal sieve depth for n=485K-490K: 3570T
Countdown to reaching the optimal sieve depth for n=490K-495K: 5050T
Countdown to reaching the optimal sieve depth for n=495K-500K: 5999.98T

Odds that a k/n pair from the n=480K-485K effort will be prime: 1 in 5175
Odds that a k/n pair from the n=480K-485K effort will be twin: 1 in 26.8 million
Odds that a k/n pair from the n=485K-490K effort will be prime: 1 in 5390
Odds that a k/n pair from the n=485K-490K effort will be twin: 1 in 29.1 million

Probability of finding a twin for the n=480K-500K, k<10M effort: 90%

Upcoming events:
April 13-18 2011: Next TPS rally

Interesting Links:
Information about twin primes: http://en.wikipedia.org/wiki/Twin_prime
Largest twin primes: http://primes.utm.edu/top20/page.php?id=1
Twin Prime Conjecture: http://mathworld.wolfram.com/TwinPrimeConjecture.html
Chronology of Twin Prime records (now outdated, but good for historical info): http://yves.gallot.pagesperso-orange...s/chrrcds.html
Smallest k that yields a twin for different n-values: http://www.rieselprime.de/Related/FirstKTwin.htm

mdettweiler · 2011-02-14, 05:41

Quote:

Originally Posted by Oddball

For TPS, sieving is best done by 64-bit computers that have at least 1GB of RAM, and you can visit this thread for further details on getting started with sieving: http://www.mersenneforum.org/showthread.php?t=12260

A slight addendum to this: currently, the 64-bit version of tpsieve does not take advantage of the SSE2 capabilities of modern CPUs. The 32-bit version, however, does--so even though 64-bit computers sieve faster than 32-bit in general, as things currently stand it is actually faster to use the 32-bit tpsieve binary on both 32-bit and 64-bit operating systems. Thus, the speed and efficiency of both are equivalent.

(Note that this will, of course, change when the 64-bit binary is eventually updated to include SSE2 support; once that happens, the 64-bit version should sieve almost twice as fast as the 32-bit version.)

Flatlander · 2011-02-14, 15:26

Quote:

Originally Posted by mdettweiler

...as things currently stand it is actually faster to use the 32-bit tpsieve binary on both 32-bit and 64-bit operating systems. Thus, the speed and efficiency of both are equivalent.
...)

http://mersenneforum.org/showpost.ph...&postcount=103

mdettweiler · 2011-02-14, 18:16

Quote:

Originally Posted by Flatlander

http://mersenneforum.org/showpost.ph...&postcount=103

Huh...that's interesting. It sounds like Oddball's X6 was faster with the 32-bit SSE2 version, whereas your i5 was faster with the 64-bit non-SSE2 version.

Anybody have an idea why this is?

JohnFullspeed · 2011-05-28, 07:56

Idea

Sample
Imagine you write a modulo fonctioon
Let A be the numberr to mod
and B the divisor and M the modulo
M:= A mod B;
This code is fine(perhaps) but it has one problem:
yoiu can't use it for real because we don't have a mod for real

So you write something like this
Real:=A
I:=A-(Round(Real /B)*B);

You run the application: strange it' more faster with
real 64 that in 64 integer ?

Because you use the FPU

It' seems that in your code you have
this kind of configuation:
using SSE4 is faster but when you don't have SSE4 the old technolgie is
So using SSE4 is wrong. The solution with SSE4 is intellectualy
just but slower.

More the techn,ologie is speed more the environnement is complex and importatnt,And if it is wrong the new tecnologie is wrong

A Indy car is good on speed way but on grass or ice

JohnFullspeed · 2011-05-29, 17:00

I'm not sure to well understood:
for me:
The projet is to compute all twins primes 5<twinx with X more than 144000 digit

The resarch is separate in range

For saller values you have found value until 490 000

So if i want to search (begining slwoly) i can reserve a range : for exampe 490 000- 1 000 000.
IO search and when the searc is ended I send yoi a file with the resucées and a little post?

I'm rigtht????

John

2011-02-14, 01:30	#1
Oddball May 2010 499 Posts	General information about this project Welcome! The Twin Prime Search (TPS) is, as you may have guessed, a project that looks for large twin primes. There are two efforts underway, which are described below. Main subproject: We're mainly focused on a variable-n search for twins that are 144,000 - 151,000 digits long. There are two ways to participate - one is sieving, and the other is LLR testing. A quick and easy to remember analogy is that sieving acts as a shotgun and LLR testing acts as a sniper rifle when it comes to removing k/n pairs. Sieving: This is a process that eliminates candidates by checking whether any of them have factors within a certain range. You will not find a twin or a prime by sieving, but choosing sieving over primality testing is often more effective in the long run. That's because you'll usually eliminate more candidates by sieving for a given period (1 day, for example) than by LLRing for the same amount of time. For TPS, sieving is best done by 64-bit computers that have at least 1GB of RAM, and you can visit this thread for further details on getting started with sieving: http://www.mersenneforum.org/showthread.php?t=12260 LLR testing: Most of the excitement and action happens here, as this is the only way to find primes and twins. LLR is a program that tests k/n pairs for primality one by one, and each candidate takes about 5 minutes to test on a single core PC. LLR testing can be done manually or automatically. Manual testing works similarly to sieving and is better suited for computers with very slow, nonexistent, or irregular internet access. More details on manual LLR reservations are here: http://www.mersenneforum.org/showthread.php?t=13387, and more details on automatic LLRing (which uses LLRnet and/or PRPnet) are here: http://www.mersenneforum.org/showthread.php?t=13805 Secondary subproject: Called "Operation Megabit Twin", this subproject searches for twins and Sophie Germain primes that are over a million binary digits long. LLR testing has not yet begun, but you can contribute to the sieve effort by heading over to http://www.mersenneforum.org/showthread.php?t=13439 and reserving a range. So if you're hoping to get a world record, want to put your computer to good use, or are simply interested in math, why not take the next step and join us? Last fiddled with by Oddball on 2011-02-14 at 01:43 Reason: moving milestones, countdowns, etc to new post

2011-02-14, 01:32	#2
Oddball May 2010 499 Posts	Historical Milestones: April 13, 2006: Project founded, n=195000 effort started Mid-November 2006: Collaboration with Primegrid starts Mid-December 2006: Sieving of n=333333 begins January 15, 2007: 20036636132^195000+/-1 twin found (58711 digits) August 6, 2009: 655164683552^333333+/-1 twin found (100355 digits) August 8, 2009: Start of variable-n search May 10, 2010: Variable-n search resumed after months of inactivity May 25, 2010: "Operation Megabit Twin" subproject begins August 30, 2010: LLRnet and PRPNet servers introduced for the variable-n search January 14-16, 2011: First TPS rally March 29, 2011: Optimal sieve depth for n=480K-485K reached Countdowns and odds (last updated 4/2/2011): Countdown to reaching the optimal sieve depth for n=485K-490K: 3570T Countdown to reaching the optimal sieve depth for n=490K-495K: 5050T Countdown to reaching the optimal sieve depth for n=495K-500K: 5999.98T Odds that a k/n pair from the n=480K-485K effort will be prime: 1 in 5175 Odds that a k/n pair from the n=480K-485K effort will be twin: 1 in 26.8 million Odds that a k/n pair from the n=485K-490K effort will be prime: 1 in 5390 Odds that a k/n pair from the n=485K-490K effort will be twin: 1 in 29.1 million Probability of finding a twin for the n=480K-500K, k<10M effort: 90% Upcoming events: April 13-18 2011: Next TPS rally Interesting Links: Information about twin primes: http://en.wikipedia.org/wiki/Twin_prime Largest twin primes: http://primes.utm.edu/top20/page.php?id=1 Twin Prime Conjecture: http://mathworld.wolfram.com/TwinPrimeConjecture.html Chronology of Twin Prime records (now outdated, but good for historical info): http://yves.gallot.pagesperso-orange...s/chrrcds.html Smallest k that yields a twin for different n-values: http://www.rieselprime.de/Related/FirstKTwin.htm Last fiddled with by Oddball on 2011-04-02 at 21:59 Reason: update

2011-05-28, 07:56	#6
JohnFullspeed May 2011 France 10100001₂ Posts	Yes Idea Sample Imagine you write a modulo fonctioon Let A be the numberr to mod and B the divisor and M the modulo M:= A mod B; This code is fine(perhaps) but it has one problem: yoiu can't use it for real because we don't have a mod for real So you write something like this Real:=A I:=A-(Round(Real /B)*B); You run the application: strange it' more faster with real 64 that in 64 integer ? Because you use the FPU It' seems that in your code you have this kind of configuation: using SSE4 is faster but when you don't have SSE4 the old technolgie is So using SSE4 is wrong. The solution with SSE4 is intellectualy just but slower. More the techn,ologie is speed more the environnement is complex and importatnt,And if it is wrong the new tecnologie is wrong A Indy car is good on speed way but on grass or ice

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2011-05-29, 17:00	#7
JohnFullspeed May 2011 France 7·23 Posts	I'm not sure to well understood: for me: The projet is to compute all twins primes 5<twinx with X more than 144000 digit The resarch is separate in range For saller values you have found value until 490 000 So if i want to search (begining slwoly) i can reserve a range : for exampe 490 000- 1 000 000. IO search and when the searc is ended I send yoi a file with the resucées and a little post? I'm rigtht???? John