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Tour de Primes 2016
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Michael GoetzVolunteer moderator Project administrator Project scientist
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Joined: 21 Jan 10 Posts: 10296 ID: 53948 Credit: 114,792,065 RAC: 103,658

Tour de Primes 2016
Welcome to the 8th annual Tour de Primes. 2 is the first prime number...and the only even one. This makes it unique among prime numbers. Therefore, February is declared Prime month...being the 2nd month of the year. :) And there's no better way to pay homage to a prime number than to go out and find one. :) More precisely, a Top 5000 prime.
For the month of February, an informal competition is offered. There are no points to be gained or awards to be won...just a simple rare jersey at the end of the month to add to your badge list. No pressure or stress other than what you put on yourself. :)
 NEW! Red Jersey  discoverer of largest prime
 Yellow Jersey  prime count leader (tiebreaker will be prime score)
 Green Jersey  points (prime score) leader
 Polkadot Jersey  on the 19th of February we'll have a "mountain" stage and award the Polkadot Jersey to the one who finds the most primes on that day (tiebreaker will be prime score for that day).
In the event of the discovery of a Sophie Germain pair or twin primes, or other discoveries that find multiple primes at once, both (or all) primes shall count towards TDP totals.
Results will be available at http://www.primegrid.com/challenge/tdp_2016.php.
As with the last few years, for all primes (BOINC and PRPNet) we're using the new reporting system whereby the prime's date of discovery determines whether it's eligible for the Tour de Primes. Prior to 2014, the date of verification for BOINC primes was used while the discovery date was used for PRPNet primes. The current system is more intuitive and fairer.
Currently, the fastest opportunities to find Top 5000 primes is with the SGS (LLR), PPSE (LLR), and GFN16 (65536) projects. Of course, should someone find a prime in the megaprime searches, this would almost guarantee the green jersey. All ports in PRPNet are also available for the competition.
To participate in BOINC SGS (LLR), PPSE(LLR), GFN16, or any other LLR or Genefer project, all you have to do is select it in your PrimeGrid preferences.
To participate in PRPNet, please see the Welcome to PRPNet thread.
We strongly recommend disabling hyperthreading, or if that's not possible, only running 50% of your cores for LLR, PFGW, and Genefer (on a CPU). I.e., anything that can find primes on a CPU. This usually produces better overall performance as well as cooler temperatures.
Good Luck, have fun, and enjoy! :D
Previous Winners
 Scott Brown
 Randall J. Scalise
 vmc
 [DPC]xRaY99_the_one_man_team
 [DPC]xRaY99_the_one_man_team
 Lonnie Christensen
 [DPC]xRaY99_the_one_man_team
 [DPC]xRaY99_the_one_man_team
 PBT_marian_boss
 Scott Brown
 Usucapio Libertatis
 Scott Brown
 shanky123
 [BOINCstats] LostBoy
 Snf*
 lennart
 lennart
 [SG]marodeur6
 lennart
 syama
 lennart
Full rankings can be seen here: 2009  2010  2011  2012  2013  2014  2015
Totals by Year
2009 2010 2011 2012 2013 2014 2015
Total Primes found 212 309 766 646 238 254 254
Total Score 457.30 2663.27 21803.72 20727.04 15614.83 20982.77 30268.46
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Please do not PM me with support questions. They will usually go unanswered. Ask on the forums instead. Thank you!
 


2 is the first prime number...and the only even one. This makes it unique among prime numbers. Therefore, February is declared Prime month...being the 2nd month of the year. :)
And in 2016, the number of days in February is right perfect. /JeppeSN  

pschoeferVolunteer developer Volunteer tester
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Joined: 20 Sep 05 Posts: 632 ID: 845 Credit: 1,436,757,892 RAC: 384,573

Of course, should someone find a prime in the megaprime searches, this would almost guarantee the green jersey.
Remember that last year even Crackenback's two PPSMEGA primes were easily outscored by Randall's PPS/SGS/PPSE mix. I'd guess that at least a SR5 or even GFN18 mega prime will be required to win the green jersey with a single prime.
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Ken_g6Volunteer developer
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Joined: 4 Jul 06 Posts: 826 ID: 3110 Credit: 98,600,815 RAC: 40,593

Currently, the fastest opportunities to find Top 5000 primes is with the SGS (LLR), PPSE (LLR), and GFN16 (65536) projects.
Can you estimate, for each of these projects, how many work units one has to do, on average, to find a prime? Maybe based on math; maybe based on the prime finding rate so far?
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Michael GoetzVolunteer moderator Project administrator Project scientist
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Joined: 21 Jan 10 Posts: 10296 ID: 53948 Credit: 114,792,065 RAC: 103,658

Currently, the fastest opportunities to find Top 5000 primes is with the SGS (LLR), PPSE (LLR), and GFN16 (65536) projects.
Can you estimate, for each of these projects, how many work units one has to do, on average, to find a prime? Maybe based on math; maybe based on the prime finding rate so far?
Not easily, no.
I think for SGS the ratio is somewhere between 1 in 10,000 and 1 in 20,000. That's just a guess based on anecdotal reports. We don't keep enough data long term in an easily acceptable format to get a good factbased estimate.
For the other small LLR projects, PPS and PPSE, we also don't keep the long term data in an easily readable form.
For larger LLR numbers, the primes are so rare that the dataset is too small to draw reasonable conclusions.
For GFN numbers, I can give you somewhat better answers because I have all the data.
Fof GFN15, since the double check ended, we've seen about 1 prime for every 8800 candidates. GFN15 isn't eligible for TDP, however.
For GFN16, since the double check ended, the ratio is 1 prime per 16,500 candidates.
For GFN17Low, the ratio is about 1 prime per 17,800 candidates.
For larger GFN numbers there are too few primes to give reliable estimates.
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tng*Send message
Joined: 29 Aug 10 Posts: 255 ID: 66603 Credit: 8,782,661,330 RAC: 7,545,668

Currently, the fastest opportunities to find Top 5000 primes is with the SGS (LLR), PPSE (LLR), and GFN16 (65536) projects.
Can you estimate, for each of these projects, how many work units one has to do, on average, to find a prime? Maybe based on math; maybe based on the prime finding rate so far?
Not easily, no.
I think for SGS the ratio is somewhere between 1 in 10,000 and 1 in 20,000. That's just a guess based on anecdotal reports. We don't keep enough data long term in an easily acceptable format to get a good factbased estimate.
An anecdotal report:
I have been running quite a few SGS tasks (several thousand a day) for a few weeks (excluding the challenge). My "Percentage of tests resulting with a prime" for SGS has varied between .034 and .0142, which is quite consisten with previous results when I was running fewer SGS tasks. Since this is both primes and double checks, that would put SGS at 1 prime in 1415 thousand tasks  right in the middle of that range.
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Michael GoetzVolunteer moderator Project administrator Project scientist
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Joined: 21 Jan 10 Posts: 10296 ID: 53948 Credit: 114,792,065 RAC: 103,658

If you're trying to find reportable primes as fast as possible, whether specifically for this challenge or in general because you like finding primes, your best bet is therefore to run GFN16 on the GPU and either SGS or PPSE on the CPU cores.
If you don't care about the primes being reportable (and counting for this challenge), put your GPU on GFN15 instead.
In both cases, you should leave one CPU core free to feed the GPU.
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Ken_g6Volunteer developer
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Joined: 4 Jul 06 Posts: 826 ID: 3110 Credit: 98,600,815 RAC: 40,593

OK, I looked at the math a little more and it should be fairly easy to figure the probability of an SGS prime. The probability that any random number N is prime is 1/ln(N). The form of the number (k*2^n+/1) eliminates half the numbers (the even ones), but k is also given to be odd. Edit: No, it's not! So, the probability that any SGS test is prime should be about:
2*(kmaxkmin)/[(the number of k's remaining after the sieve)*ln(k*2^n)]
I assume you have all those numbers? Is my math right? "k" should probably be any recent k; mainly the order of magnitude matters.
The other types are a little harder to figure out, because they vary by n, not k, so their probability varies more widely.
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GDBSend message
Joined: 15 Nov 11 Posts: 138 ID: 119185 Credit: 627,386,179 RAC: 5,499,208

Currently, the fastest opportunities to find Top 5000 primes is with the SGS (LLR), PPSE (LLR), and GFN16 (65536) projects.
Can you estimate, for each of these projects, how many work units one has to do, on average, to find a prime? Maybe based on math; maybe based on the prime finding rate so far?
Not easily, no.
I think for SGS the ratio is somewhere between 1 in 10,000 and 1 in 20,000. That's just a guess based on anecdotal reports. We don't keep enough data long term in an easily acceptable format to get a good factbased estimate.
For the other small LLR projects, PPS and PPSE, we also don't keep the long term data in an easily readable form.
For larger LLR numbers, the primes are so rare that the dataset is too small to draw reasonable conclusions.
For GFN numbers, I can give you somewhat better answers because I have all the data.
Fof GFN15, since the double check ended, we've seen about 1 prime for every 8800 candidates. GFN15 isn't eligible for TDP, however.
For GFN16, since the double check ended, the ratio is 1 prime per 16,500 candidates.
For GFN17Low, the ratio is about 1 prime per 17,800 candidates.
For larger GFN numbers there are too few primes to give reliable estimates.
From the sieve stats for GFNWR (n=22) you can make a reasonable guesstimate. There was an estimate of 5 GFNWR primes existing thru the OCL2 test range. The current sieve has 4.75 million entries thru the OCL3 + OCL2 range. That means the odds of finding a GFNWR is about 1 in a million.
With such poor odds of finding a GFNWR, you're better off searching for smaller primes. If you want to help find GFNWR primes in our lifetime and have an Nvidia GPU, the best thing you can do now is to run manual sieves for n = 22. For the time spent checking a single number via GFN, you could eliminate 300+ nonprime entries via manual sieve.
 

axnVolunteer developer Send message
Joined: 29 Dec 07 Posts: 256 ID: 16874 Credit: 16,170,582 RAC: 73,500

OK, I looked at the math a little more and it should be fairly easy to figure the probability of an SGS prime. The probability that any random number N is prime is 1/ln(N). The form of the number (k*2^n+/1) eliminates half the numbers (the even ones), but k is also given to be odd. Edit: No, it's not! So, the probability that any SGS test is prime should be about:
2*(kmaxkmin)/[(the number of k's remaining after the sieve)*ln(k*2^n)]
I assume you have all those numbers? Is my math right? "k" should probably be any recent k; mainly the order of magnitude matters.
The other types are a little harder to figure out, because they vary by n, not k, so their probability varies more widely.
This doesn't work for SGS  it is a quadsieve (sieving 4 forms simultaneously). Only 1 in million k survives (just a guess). If we applied the formula, it will inflate the probability. The correct formula is 1.781*ln(p)/ln(k*2^n) where p is the sieve depth.  


For GFN numbers, I can give you somewhat better answers because I have all the data.
For GFN15, since the double check ended, we've seen about 1 prime for every 8800 candidates.
For GFN16, since the double check ended, the ratio is 1 prime per 16,500 candidates.
For GFN17Low, the ratio is about 1 prime per 17,800 candidates.
For larger GFN numbers there are too few primes to give reliable estimates.
We can apply the formula log(n) / (e^gamma * log(p_max)), where n is the candidate, p_max is the sieve depth and gamma is Euler's constant 0.577215665.
(see http://www.primegrid.com/sieving/gfn/)
GFN15: 32768*log(18800000.0) / (1.781 * log(1100.0*10^15)) = 7400.
GFN16: 65536*log(5850000.0) / (1.781 * log(10762.0*10^15)) = 13000.
GFN17: 131072*log(2300000.0) / (1.781 * log(8696.0*10^15)) = 24700.
GFN18: 262144*log(1350000.0) / (1.781 * log(20001.0*10^15)) = 46700.
GFN19: 524288*log(950000.0) / (1.781 * log(19100.0*10^15)) = 91300.
GFN20: 1048576*log(730000.0) / (1.781 * log(37400.0*10^15)) = 176000.
 

yank Send message
Joined: 14 May 07 Posts: 90 ID: 8367 Credit: 4,373,336,451 RAC: 5,930,962

Need some recommendation for the setup of my computers for the 'Tour de Primes.
Have HT turn off...will have the video cards for the GFN16 work units? For the SGS LLR and
PPSE LLR work units will have only 4 CPU's working. Or should I have 5 or 6 or 7 or 8 CPU's
working?  

Michael GoetzVolunteer moderator Project administrator Project scientist
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Joined: 21 Jan 10 Posts: 10296 ID: 53948 Credit: 114,792,065 RAC: 103,658

Need some recommendation for the setup of my computers for the 'Tour de Primes.
Have HT turn off...will have the video cards for the GFN16 work units? For the SGS LLR and
PPSE LLR work units will have only 4 CPU's working. Or should I have 5 or 6 or 7 or 8 CPU's
working?
For the best chance of finding a prime...
1) Set GPUs to GFN16.
2) Set CPUs to SGS or PPSE.
3) Turn off hyperthreading.
4) Leave 1 core free to service the GPU. E.g., with a desktop Corei7, set the BOINC setting to "use 75.00% of CPUs" so that 3 cores are used, leaving the 4th free for the GPU.
Alternative strategy for hyperthreaded CPUs: (Theoretical and untested, use at your own risk)
1 & 2: As above
3) Leave hyperthreading on.
4) Set "Use CPUs" to 50%, allowing 4 cores to crunch LLR and 1 hyperthread to service the GPU. Not sure how well this will work...
Alternative #2: (For advanced users only; don't bother asking me how to do it.)
0) Use app_info to run OCL4 which doesn't hog a CPU core.
1 & 2: As above.
Run LLR on 4 cores.
Not sure if HT on or off is better in this scenario.
____________
Please do not PM me with support questions. They will usually go unanswered. Ask on the forums instead. Thank you!
 

Keith Send message
Joined: 8 Dec 13 Posts: 196 ID: 284516 Credit: 142,566,700 RAC: 162,393

Alternative strategy for hyperthreaded CPUs: (Theoretical and untested, use at your own risk)
1 & 2: As above
3) Leave hyperthreading on.
4) Set "Use CPUs" to 50%, allowing 4 cores to crunch LLR and 1 hyperthread to service the GPU. Not sure how well this will work...
I am running SGS and a combination of GFN16, 17 low, 18 and 19 right now on my system with an i7 4790 and a GTX760.
I have hyperthreading ON and have the "Use CPUs" to 50%. This lets me run 4 workunits on the CPU and one on the GPU at the same time using ~63% of my CPU. My system appears to be rather stable for this (one or two hiccups due to a faulty power supply I just replaced).
The SGS units were averaging about 580 seconds per unit without a GPU unit running vs 720 seconds per unit with a GPU unit running. That's an increase of ~25%.
Doing the math on this, to do 12 units (12 because equally divisible by 4 and 3) doing three units at a time would be four sets of three to get to 12 and 4*580=2320 seconds. Doing three sets of four to get to 12 would be 3*720=2160 seconds. So running 4 CPU and 1 GPU with HT ON is slightly faster when SGS is the CPU project in question.
Other CPU based projects may react differently to the way I'm running.
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My Primes
Badge Score: 4*4 + 5*10 + 8*2 + 9*1 = 91
 

Michael GoetzVolunteer moderator Project administrator Project scientist
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Joined: 21 Jan 10 Posts: 10296 ID: 53948 Credit: 114,792,065 RAC: 103,658

Just to mix things up a bit, we're going to add a "Red Jersey" award this year. As per Scott's suggestion from last year, this new jersey (not to be confused with "New Jersey", which is substantially more blue than red) will be awarded to the discoverer of the largest prime during the month of February.
I'll be adjusting the relevant forum posts and the results page in the next day or two.
Adjust your plans accordingly, and good luck!
____________
Please do not PM me with support questions. They will usually go unanswered. Ask on the forums instead. Thank you!
 

Van ZimmermanVolunteer moderator Project administrator Volunteer tester Project scientist Send message
Joined: 30 Aug 12 Posts: 1768 ID: 168418 Credit: 4,253,460,853 RAC: 4,530,177

Just to mix things up a bit, we're going to add a "Red Jersey" award this year. As per Scott's suggestion from last year, this new jersey (not to be confused with "New Jersey", which is substantially more blue than red) will be awarded to the discoverer of the largest prime during the month of February.
I'll be adjusting the relevant forum posts and the results page in the next day or two.
Adjust your plans accordingly, and good luck!
Not all of it :)
https://gregorynaigles.files.wordpress.com/2015/07/nj14senresults.png?w=400&h=566  

Michael GoetzVolunteer moderator Project administrator Project scientist
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Joined: 21 Jan 10 Posts: 10296 ID: 53948 Credit: 114,792,065 RAC: 103,658

Just to mix things up a bit, we're going to add a "Red Jersey" award this year. As per Scott's suggestion from last year, this new jersey (not to be confused with "New Jersey", which is substantially more blue than red) will be awarded to the discoverer of the largest prime during the month of February.
I'll be adjusting the relevant forum posts and the results page in the next day or two.
Adjust your plans accordingly, and good luck!
Not all of it :)
https://gregorynaigles.files.wordpress.com/2015/07/nj14senresults.png?w=400&h=566
I didn't say all of it; just a majority of it. And I'll stand by that assessment...
Since rural counties tend to vote conservative, and urban counties (i.e., cities) tend to vote liberal, if you look at a county by county map it's usually going to look very red because acre by acre, more land is occupied by people who tend to be more conservative.
But acres don't vote. People vote.
In the 2012 Presidential election, the blues beat the reds 58% to 41% in NJ. In 2008, it was 57% to 42%. 2004 was 53 to 47%. You have to go back to 1988, when Bush beat Dukakis, for the last time NJ cast its electoral votes for a Republican.
Source: http://www.electoralvote.com/evp2016/Info/elections1900to2012.xlsx
Oh, yeah, last thing. Since the map you linked to was a map of the 2014 Senate race, it should be noted that Cory Booker, the "blue" candidate on that map, won that election by 55% to 42%. If you're counting votes rather than acres, that map is still more blue than red. :)
Source: https://en.wikipedia.org/wiki/United_States_Senate_election_in_New_Jersey,_2014
Pixels aside, I'll stick with my initial assertion.
Unless, of course, you're looking at this guy's maps:
http://uselectionatlas.org/RESULTS/index.html
He uses red for the Democrats and blue for the Republicans. Go figure.
(Now, if you wanted to make a better argument about New Jersey, you could use the recent gubernatorial elections.)
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Please do not PM me with support questions. They will usually go unanswered. Ask on the forums instead. Thank you!
 


Pixels: This Jersey is not confused with New Jersey. /JeppeSN  


I approve of adding a new jersey.
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Who is going to New Jersey? I don't live to far from there. Gas is cheap any way.  

Van ZimmermanVolunteer moderator Project administrator Volunteer tester Project scientist Send message
Joined: 30 Aug 12 Posts: 1768 ID: 168418 Credit: 4,253,460,853 RAC: 4,530,177

I didn't say all of it; just a majority of it. And I'll stand by that assessment...
We do happen to have a 2term governor somewhat of the "red" persuasion.
And I absolutely agreethe population of the state is concentrated in more urban areas, and there is good correlation with that population density and the "blueness" of a municipality. Not all of us are in (or near) those blue areas, which was all I was saying, or at least attempting to say :)
 

Van ZimmermanVolunteer moderator Project administrator Volunteer tester Project scientist Send message
Joined: 30 Aug 12 Posts: 1768 ID: 168418 Credit: 4,253,460,853 RAC: 4,530,177

Who is going to New Jersey? I don't live to far from there. Gas is cheap any way.
1.53/gallon regular 1.61/gallon diesel is as cheap as I've seen.
 

Michael GoetzVolunteer moderator Project administrator Project scientist
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Joined: 21 Jan 10 Posts: 10296 ID: 53948 Credit: 114,792,065 RAC: 103,658

Who is going to New Jersey? I don't live to far from there. Gas is cheap any way.
1.53/gallon regular 1.61/gallon diesel is as cheap as I've seen.
It's always a good 40 cents a gallon cheaper in NJ than in NY.
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Please do not PM me with support questions. They will usually go unanswered. Ask on the forums instead. Thank you!
 


Who is going to New Jersey? I don't live to far from there. Gas is cheap any way.
1.53/gallon regular 1.61/gallon diesel is as cheap as I've seen.
In Greece, we have 3.8 liters/US gallon x 1.33 euro/liter x 1.092 USD/euro = $5.52/gallon. Things were much worse when the euro was trading at 1.40 USD/euro.
Only in my dreams will I see US pricing here in Greece.  


May I have a recommendation please on my Corei7 if I want to run CPU only, NO GPU, leaving the machine idle for the entire month to run this challenge only. Hyperthreadding setting? Which app? and only 1 app or more than 1? What other settings (such as auto updates, etc. turned off) if I desire to leave this machine unattended. I would peek at its progress from another machine.
Thx
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Michael GoetzVolunteer moderator Project administrator Project scientist
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Joined: 21 Jan 10 Posts: 10296 ID: 53948 Credit: 114,792,065 RAC: 103,658

May I have a recommendation please on my Corei7 if I want to run CPU only, NO GPU, leaving the machine idle for the entire month to run this challenge only. Hyperthreadding setting? Which app? and only 1 app or more than 1? What other settings (such as auto updates, etc. turned off) if I desire to leave this machine unattended. I would peek at its progress from another machine.
Hyperthreading OFF, or run 50% of the cores if HT must be left on. In other words, run 4 cores.
Best bet is to run SGS.
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Michael GoetzVolunteer moderator Project administrator Project scientist
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The 2016 Tour de Primes has officially started! Good luck everyone!
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Michael GoetzVolunteer moderator Project administrator Project scientist
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Joined: 21 Jan 10 Posts: 10296 ID: 53948 Credit: 114,792,065 RAC: 103,658

This is the reason I wanted these charts. :)
I've always assumed there would be changes in usage patterns during challenges. Now there's data.
From the charts on http://www.primegrid.com/server_status_tasks.php:
Looking at "LLR tasks in Progress", SGS has a small but distinct increase right at the start of TDP. PPSE has a slow increase around the start, but it's not as abrupt.
But if you look at "GFN tasks in Progress", there's a significant and abrupt increase at exactly 00:00 on February 1st in GFN16, GFN17Low, and GFN17Mega. GFN15, which isn't eligible for TDP, is flat.
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Michael GoetzVolunteer moderator Project administrator Project scientist
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Curious about the process of what happens after your computer returns a prime? Did you notice that primes that show up on the TDP leader boards may be several days old even though they just became visible? Here's the behindthescenes look at what happens to primes when they're discovered:
BOINC:
1) If it's not a mega prime, you wait for your wingman to return a result that also says the number is prime. It's very rare for a computation error to result in a false prime indication, EXCEPT when b=2 and c=1. That affects SGS, TRP, Woodall, and some 321 tests. With the algorithm used for those numbers, computation errors frequently result in false primes. We don't get excited about those primes until the wingman returns the same result since it's often just someone with too much overclocking.
2) If it IS a mega prime, we speed up the wingman process a bit by verifying the prime on our own computers. We also run it through PFGW just in case there's a bug in LLR.
2a) If b=2 and c=1, we also start checking for Fermat divisors on our computers. The server will do this automatically, but our computers are several times faster. (No AVX on the servers.)
2b) Finally, once we've verified the prime ourselves, we inhibit additional wingmen for the mega prime. The wingman who is currently running can finish his task and become the official double checker, but if he doesn't, no other tasks gets sent out. This means we don't have to wait months and months for a wingman to verify the prime.
3) Once the wingman verifies the prime (or we do it, as in 2b above), the server then does additional testing on some primes. As mentioned above, we check for Fermat divisors on numbers where b=2 and c=1, and on SGS primes we check for Sophie Germain pairs by checking k*2^(n1)1 and k*2^(n+1)1 on the server. Your computer would have already done an additional check for a twin prime by checking k*2^n+1.
3a) For GFN "primes", your computer is actually doing a "probable prime" (PRP) test, not a primality test. When your computer finds a GFN probable prime, a primaliity test is then done on the server to prove primality. Although this is automatically run by the server after the wingman validates the initial result, Jim or myself often start the primality test manually on the server to give it a headstart as soon as we notice that the first computer has returned a probable prime result. Note that for GFN18 and higher, we run the primality test manually on one of our own computers. The servers, lacking AVX/FMA3, take too long to do such long tests.
4) Once the additional checks are done in either 2a, 3, or 3a, we're ready to report the prime. If you have set your PrimeGrid preferences to permit PrimeGrid to report the primes for you, we will do so. Unless there's a specific reason that you want to report it yourself, we recommend you let us do it. It's easy to make mistakes and you need to know which programs and projects you should be listing as contributing to the prime discovery. We've got that all automated and it's much easier for us to do it. We'll create your account, set up the proof codes, etc.
4a) If you haven't given us permission to report for you, we notify you by email and you have to report the prime yourself. We will make every effort to get in contact with you but if 19 days go by and we can't reach you, we'll let the double checker report the prime instead. If the double checker hasn't given us permission to report the prime, and we can't reach him or her within an additional 19 days, then PrimeGrid will report the prime itself anonymously.
4b) If the prime is too small to report to T5K, the server automatically marks the prime as "reported". No actually reporting is done. Currently this only applies to GFN15 primes, although sometime in late 2016 or 2017 SGS will also be too small for reporting.
5) After the prime is submitted, the prime is verified by the Top 5K website. Once it's been verified, it shows up on their list.
6) Periodically, (currently twice per hour), our server looks at the list on the Top 5K website and makes note of any new primes, and marks them as "reported" in our database. Once they're marked as reported, they can be displayed.
7) A few minutes after we check Top 5K, we put newly reported primes into another, permanent part of our database. This is when primes will show up on most of the other parts of the website. (This is the point where primes will show up on the Tour de Primes leaderboard.)
PRPNet:
1) Mostly the same as BOINC, except that there's no wingman and we do everything by hand. We double check the prime manually on either our own computers or on one of the servers.
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Ken_g6Volunteer developer
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Joined: 4 Jul 06 Posts: 826 ID: 3110 Credit: 98,600,815 RAC: 40,593

I have a confession to make. I'm participating in the Tour de Primes with the help of concealed motors! Particularly in my fans and hard drives.
Please don't ban me! :P
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I have a confession to make. I'm participating in the Tour de Primes with the help of concealed motors! Particularly in my fans and hard drives.
Please don't ban me! :P
I don't think you should be banned. But maybe any prime you find that has a digit with a wheellike shape should be excluded. ;)
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Is there a lag between misc prime listing pages & emails?
I received email about 2.5hrs ago about "Added 120994 : 2510221597767*2^12900001 (388342 digits)" with this WU of which this is my task, sent on Jan 31, received on Feb 1.
As such, since returned on Feb 1, I would think that it would be included in the challenge. But, looking at http://www.primegrid.com/challenge/tdp_2016.php, I see other primes reported on Feb 1st with the same number of digits, but not the one I was emailed about.
Also, strangely, I see in my "Your Account" page that I found 3 primes through SGS, yet clicking the "3" link ends up showing me only two primes, none of which is this latest one.
A post earlier said "Once an hour, our server looks at the list on the Top 5K website and makes note of any new primes, and marks them as "reported" in our database. Once they're marked as reported, they can be displayed." Does this mean 2.5hrs after the email is fair time to wait?
Basically, what is the expected delta between a prime being reported by a host TO showing up on the user's account page TO showing up on their primes page TO showing up on the challenge page?
Thanks
Tuna
EDIT: Email plus 2h45m is when all the pages caught up. Still curious as to what drives that wide range of delays given that many other Feb 1 primes were found.
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Can someone please explain why all seven SGS primes discovered in this event to date have the identical number of digits, 388,342 ???
I seem to have found one of these as doublechecker which is posted to the scorecard.
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JimBVolunteer moderator Project administrator Project developer Send message
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Basically, what is the expected delta between a prime being reported by a host TO showing up on the user's account page TO showing up on their primes page TO showing up on the challenge page?
When we report a prime to T5K, it doesn't show up there until that site verifies it. At the moment, there seems to be a single thread doing that testing. So if we or someone else reports a large prime, it may take hours or even more than a day for them to retest that candidate using PFGW (their preferred program). After a prime is verified, it shows up on the next rebuild of their list at something like 21 minutes after the hour. We download the list at 30 minutes after the hour and use that to control whether to show the prime publicly.
It might also happen that we (meaning I) report a bunch of primes at once. With only one being tested at a time, it might take hours for T5K to get through them all. Plus, others are also reporting primes though PrimeGrid is responsible for more current additions than anyone else.  


Thanks, Jim. That explains the delta between finding it and getting the email. What is the 2h45m from email to misc pages here getting updated? Not that it bothers me. Just curious.
 

JimBVolunteer moderator Project administrator Project developer Send message
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Can someone please explain why all seven SGS primes discovered in this event to date have the identical number of digits, 388,342 ???
I seem to have found one of these as doublechecker which is posted to the scorecard.
All our primes found in the SGS subproject are of the form k*2^12900001 where k is currently 13 digits long at around 2.5 trillion. Given all the candidates we have to test in order to find a prime, the length increases very slowly. Take a look at the full Top5K list at http://primes.utm.edu/primes/lists/all.txt and all the primes from (currently 3510th to 5000th place are those primes. There are about 1500 primes there and they're all either 388341 or 388342 digits long.  

JimBVolunteer moderator Project administrator Project developer Send message
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Thanks, Jim. That explains the delta between finding it and getting the email. What is the 2h45m from email to misc pages here getting updated? Not that it bothers me. Just curious.
That's what I explained above. The email goes out about 10 seconds after I report the prime. Everything else is the delay on them testing and the fact that the Top5K list is only updated once an hour (so we only check it once an hour).
Mike's post above talks about other delays after validation but before reporting to Top5K.  

Michael GoetzVolunteer moderator Project administrator Project scientist
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Thanks, Jim. That explains the delta between finding it and getting the email. What is the 2h45m from email to misc pages here getting updated? Not that it bothers me. Just curious.
That's what I explained above. The email goes out about 10 seconds after I report the prime. Everything else is the delay on them testing and the fact that the Top5K list is only updated once an hour (so we only check it once an hour).
Mike's post above talks about other delays after validation but before reporting to Top5K.
Also, in the case of GFN primes, there are some optimizations in the process that Jim and I perform, and one of them is being able to report the prime before the wingman finishes. However, due to the mechanics of how the TDP leaderboard has to work, primes can't show up on the leaderboard until after task is completely validated  and that means waiting for the wingman. Since the wingman has several days to run the task, with GFN's you may be emailed aboiut the prime, and the prime reported, several days before it shows up on the TDP leaderboards.
Rest assured, however, that all primes that are eligible for TDP will be on the leaderboards. As with all things related to finding large primes, patience is required. :)
Reminder: GFN15 primes are too small to be reportable on the T5K website and are therefore NOT eligible for this challenge!
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Here's a thought, once someone wins a particular jersey, they are not eligible for THAT jersey the following year and must race for a different jersey then (unless he/she wins them all and thus can't play for any the following year). I figure Scott Brown would be most effected by this, but it would open up the door for someone else to win that particular jersey the following year. Thoughts?
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Largest Primes to Date:
As Double Checker: SR5 109208*5^1816285+1 Dgts1,269,534
As Initial Finder: SR5 243944*5^12585761 Dgts879,713
 

RafaelVolunteer tester
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Here's a thought, once someone wins a particular jersey, they are not eligible for THAT jersey the following year and must race for a different jersey then (unless he/she wins them all and thus can't play for any the following year). I figure Scott Brown would be most effected by this, but it would open up the door for someone else to win that particular jersey the following year. Thoughts?
Looking at the winners from previous years, this doesn't seem to affect Scott at all (unless he wins Yellow Jersey 2016). It only really affects lennart and... you_known_who,_with_it's_huge_and_ummemorizeable_name (#too lazy to copypaste it). Honestly, let them compete if they want to.  

Michael GoetzVolunteer moderator Project administrator Project scientist
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Here's a thought, once someone wins a particular jersey, they are not eligible for THAT jersey the following year and must race for a different jersey then (unless he/she wins them all and thus can't play for any the following year). I figure Scott Brown would be most effected by this, but it would open up the door for someone else to win that particular jersey the following year. Thoughts?
My first thought is "You want us to punish our best contributors???"
My second thought is that this has only happened twice, in 2009/2010 and in 2013/2014, and the two people who did so are no longer active.
My third thought is that of the four jerseys, this only really applies to the yellow and green. Red and polkadot have too much chance involved, and no amount of computing power is going to overcome, for example, the sheer luck of finding a 2.5 million digit prime on your 16th task.
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Here's a thought, once someone wins a particular jersey, they are not eligible for THAT jersey the following year and must race for a different jersey then (unless he/she wins them all and thus can't play for any the following year). I figure Scott Brown would be most effected by this, but it would open up the door for someone else to win that particular jersey the following year. Thoughts?
Until the Tour de France starts barring cyclists who win from competing the following year, I think we should keep the annual competition open to all.
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Proud member of Team Aggie the Pew
"Wir müssen wissen. Wir werden wissen."
"We must know, we shall know."
 David Hilbert, 1930  


For a moment I thought I had found a Proth Prime, but apparently I was just the double checker... Had to dig around a bit, but eventually I saw that the prime was discovered by another user.  


For a moment I thought I had found a Proth Prime, but apparently I was just the double checker... Had to dig around a bit, but eventually I saw that the prime was discovered by another user.
How did you dig to find that out?  


For a moment I thought I had found a Proth Prime, but apparently I was just the double checker... Had to dig around a bit, but eventually I saw that the prime was discovered by another user.
How did you dig to find that out?
I went to PrimeGrid Primes by Project and looked for the same prime as in my own list of primes found. The discoverer is tng*.  


Thanks.  

Michael GoetzVolunteer moderator Project administrator Project scientist
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There seems to be some confusion, as I've received several questions asking "why doesn't my prime show on on the Tour de Primes list" for primes that are not eligible.
A prime must be discovered by you during the month of February in order to be part of the Tour de Primes. It doesn't matter when the wingman verified the prime. It doesn't matter when you received notification by email. It doesn't matter when the prime was reported to Chris Caldwell's Top 5000 website. All that matters is when YOUR computer returned the result to the server.
If your computer returned the result in January, even if the wingman returned the result in February, the prime is NOT eligible.
P.S. Please note that that email notification that you receive does not tell you the date and time of your discovery. You need to check the time in the workunit. Thank you.
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mackerelVolunteer tester
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I'm a little surprised that I've found a PPSE and SGS already, especially as I'm not trying to! My plan was to push my luck and go large. Anyway, that gave me a thought for yet another new jersey: one for most different types of prime found.
Currently there are at least two others with 2 different types of prime. Some sort of tie break would be required. Maybe by total score, or to give a twist, the total score of the top prime of each type for each user, again promoting the variety in prime types and not just farming the more frequent types.  

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I got my annual prime reported today. Now once again trying to find a big one. 8)
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Michael GoetzVolunteer moderator Project administrator Project scientist
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There's a GFN17Low PRP in the pipeline. Assuming it verifies, which is very likely, it will be the largest prime found so far during TDP. It will probably be about 24 hours until it appears on the leader boards.
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It'll be the largest until my PPSMega prime comes through! (He said confidently, disregarding statistics)
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PrimeGrid Challenge Overall standings  Last update: From Pi to Paddy (2016)
 


I am very pleased so far in this challenge as finder of my first SGS prime. I also have another SGS prime as doublechecker. Not bad for five days effort. Onward and upward!
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Then I could come along & blow you all out the water with my 321fest.  

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Seems like I've had problems keeping all my machines running this year. One I installed Windows 10 on and it insisted on rebooting. Another I installed Xubuntu on, which installed BOINC 7.6.6 for some reason, and led to this bug. So if you have a stock Ubuntu install you might want to downgrade to BOINC 7.2.42.
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When do the stats for number of primes found get updated each day?
Comparing what the primegrid site shows with what bok's stats at FreeDC.org shows there is a discrepancy for my tally. PG is missing 2 each SGS and PPS_LLR primes at the time of writing this.
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Michael GoetzVolunteer moderator Project administrator Project scientist
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When do the stats for number of primes found get updated each day?
Comparing what the primegrid site shows with what bok's stats at FreeDC.org shows there is a discrepancy for my tally. PG is missing 2 each SGS and PPS_LLR primes at the time of writing this.
They're updated continuously  but effectively they're updated only at 30 minutes after the hour because T5K only updates once an hour.
EDIT: I just went through all the primes by hand, and your three that are showing on the TDP leader board are correct. Any other number is incorrect.
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bok says:
I just report on what is exported in the user_work file. For you this shows the following for those projects
<subproject name="Sophie Germain Search">
<workunits>38458</workunits>
<primes>9</primes>
<credit>907686.4108454467</credit>
</subproject>
<subproject name="PPS_LLR">
<workunits>105793</workunits>
<primes>17</primes>
<credit>1979625.0895292375</credit>
</subproject>
Quote Originally Posted by vaughan
Hi bok,
Could you check the number of primes found in my Primegrid stats please?
See: http://www.primegrid.com/forum_threa...rap=true#91957
I have 3 primes in the 2016 Tour de Primes challenge but I have watched my count of primes increase by 2 each this weekend for SGS and PPS_LLR, so that implies I should have 7 new primes this month. However, Michael Goetz says his count is correct (3).
See also: http://www.primegrid.com/challenge/tdp_2016.php
Thanks,
Vaughan
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Michael GoetzVolunteer moderator Project administrator Project scientist
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Bok's numbers, while correct per se, are completely useless for your purpose. You can't use them to see how many TDPeligible primes you have. The ONLY authoritative source is PrimeGrid's TDP leaderboard page.
There's two reasons FreeDC (or any other source) is going to give you misleading information:
1) The count of primes that we make public includes ALL primes you've found, including primes where you're the doublechecker. You've been the double checker on several primes in the last couple of days, so that's most likely the reason why FreeDC shows you as having found some primes while nothing shows up on the TDP Leaderboard. Those primes don't count. If you had found primes, we would have sent you an email for each one  and that happens before they show up on the leaderboard.
2) FreeDC's statistics don't show when the primes were found. Primes you may have found at the end of January may not show up on Bok's site until February. He can't tell the difference betweens primes found in February (which ARE eligble for TDP) and primes found in January but not made public until February (which are NOT eligible.)
You may discover a prime in January, but we must wait for the wingman to return his task to be validated against yours, and then our server needs to test the prime to see if it's a Fermat divisor or an SGS pair or twin prime, then Jim needs to wake up from his nap and submit it to T5K, and then T5K needs to test it themselves before adding the prime to their list, and then  and only then  do we make the prime public.
(The prime count that Bok can see goes up right after the wingman's task comes back  so that's when Bok sees that a prime was found. He can't, however, tell if you're the prime finder of the double checker. The prime itself isn't made public until after all the other steps are completed.)
Several days may pass between when you find a prime and when it can finally be made public. Therefore, FreeDC may first see your prime count go up today because of primes found days or even weeks ago.
Only primes returned to our server during the month of February count. Primes returned in January  even if you don't see them until February  do NOT count.
No computer system except PrimeGrid's server has the necessary information to know when the primes were returned, so the ONLY authoritative source for which primes are eligible for the Tour de Primes is the PrimeGrid TDP leaderboard webpage. Any other source is going to give you misleading information.
EDIT: Take a look at your primes page. In the "prime finders" section on top, you'll see your three primes that were found during February. Those are the ones that count for TDP. (That page is now showing dates for primes found recently.) Then scroll down to the double checker section. You'll see 6 primes where you were the double checker that were found during February.
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Thank you for the explanation.
I would add that I only recommenced running PrimeGrid in February after a very long break whilst I ran other projects such as SRBase. Thus any primes found were from the current Tour de Primes run. However, I accept your point that bok's data includes primes where I was the double checker. I wasn't aware of this process having just observed that his figures increased yet I didn't get the prime notification email(s) or see the official PG stats page display the new primes. The process is clearer to me now.
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Michael GoetzVolunteer moderator Project administrator Project scientist
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The red jersey will be changing hands shortly...
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The red jersey will be changing hands shortly...
Congrats golfer!  

Michael GoetzVolunteer moderator Project administrator Project scientist
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The effect of challenges on the number of primes found each day:
+++
 date  count(*) 
+++
 20160101  4 
 20160102  8 
 20160103  5 
 20160104  6 
 20160105  10 
 20160106  13 
 20160107  5 
 20160108  2 
 20160109  2 
 20160110  2 
 20160111  8 
 20160112  2 
 20160113  4 
 20160114  1 
 20160115  4 
 20160116  3 
 20160117  2 
 20160118  4 
 20160120  4 
 20160121  3 
 20160122  4 
 20160123  5 
 20160124  3 
 20160125  8 
 20160126  9 
 20160127  3 
 20160128  7 
 20160129  5 
 20160130  8 
 20160131  7 
 20160201  11 
 20160202  14 
 20160203  18 
 20160204  15 
 20160205  19 
 20160206  12 
 20160207  12 
 20160208  9 
 20160209  8 
 20160210  8 
+++
So there's a large jump in the number of primes found during February. That's obviously expected. What's also interesting is the obvious spike on January 5th and 6th. Those are the two days right before January's GFN challenge. It looks like a bunch of pwople switched from their longrunning tasks to shorter tasks like PPSE, SGS, and GFn15 or GFN16 so their computers would be ready to go at the start of the challenge.
Average primes per day for two days prior to January challenge: 11.5
Average primes per day during January challenge: 3.3
Average primes per day during February: 12.6
Average primes per day during the other days in January: 5.2
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Michael GoetzVolunteer moderator Project administrator Project scientist
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What effect does the Tour de Primes have?
We're almost half way through TDP, and so far 25 GFN16 primes have been found in the first two weeks of February.
In the previous five years PrimeGrid had discovered only 54 GFN16 primes. Slightly less than one third of all the GFN16 primes we've ever discovered have come during the first half of this year's TDP!
Perhaps a more even comparison would be comparing January to February.
In January, we discovered 13 GFN16 primes as compared to the 25 discovered in the just the first half of February.
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I think you write GFN15 a couple of places where you mean GFN16. /JeppeSN  

Michael GoetzVolunteer moderator Project administrator Project scientist
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I think you write GFN15 a couple of places where you mean GFN16. /JeppeSN
Thanks. Fixed.
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Michael GoetzVolunteer moderator Project administrator Project scientist
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I sense a disturbance in the Force...
Expect the red and green jerseys to change ownership soon.
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I sense a disturbance in the Force...
Expect the red and green jerseys to change ownership soon.
I really hope this is a prime from one of the conjecture projects. Fingers crossed.
____________
 


The number of GFN18 primes has changed...
http://www.primegrid.com/stats_genefer.php
____________
 

Michael GoetzVolunteer moderator Project administrator Project scientist
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The number of GFN18 primes has changed...
http://www.primegrid.com/stats_genefer.php
It's now been confirmed and reported: 1415198^262144+1
It will probably take another day for the prime to be verified on T5K's site. Once that happens, the prime will show up here in the various places where primes are displayed, including on the TDP leaderboards.
Congratulations to boss for finding the first GFN 262144 (or higher) prime since 2012!
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The number of GFN18 primes has changed...
http://www.primegrid.com/stats_genefer.php
It's now been confirmed and reported: 1415198^262144+1
It will probably take another day for the prime to be verified on T5K's site. Once that happens, the prime will show up here in the various places where primes are displayed, including on the TDP leaderboards.
Congratulations to boss for finding the first GFN 262144 (or higher) prime since 2012!
Nooooooooooo......... and to think that it could have been my iGPU (or my 970) if I was letting it crunch 24/7 instead of only from 0~5 AM.
Thanks for the "Good luck!" you gave me on the other thread Michael. Worked real nice.......................
Still, I'm happy that we did it.
 

Scott BrownVolunteer moderator Project administrator Volunteer tester Project scientist
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So, as we approach the mountain stage in a few hours and stand about twothirds through the 2016 TDP, you may feel that you are out of the running for the yellow jersey for the most primes and be thinking what are my chances at that green jersey...interestingly, the green jersey has had an extremely variable set of outcomes across all the previous TDP:
In 2010 and 2013, there was no mega prime found in the TDP, and the yellow jersey winner took home the green jersey as well (i.e., the "brute force" approach).
On the other hand, in 2009, there was no mega prime found, but the yellow jersey winner was beat out for the green jersey by another cruncher (i.e., the "crunch for midsized" primes approach).
Finding a mega prime won the day in both 2011 and 2012, but not just any mega prime would do in either of those years. In 2011, a 321 mega prime beat out a GFN18 mega prime; in 2012, a GFN18 mega prime beat out both a 121 mega prime and a 27 mega prime (i.e., the "go big or go home" approach).
In 2014, we had yet another result where the yellow jersey winner beat out an SR5 mega prime find (i.e., "brute force" beat "go big or go home").
2015 offered yet another result pattern where a single cruncher found TWO PPS mega primes and still lost the green jersey, but this time it was to someone other than the yellow jersey winner (i.e., "crunch for midsized" beat "go big or go home")!
So what will it be this year? A repeat of one of these former patterns? Or will it be something new yet again? No matter what, the bottom line is this: despite the recent find of a GFN18 mega prime, the green jersey is most definitely still in play!!!
 

RafaelVolunteer tester
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So, as we approach the mountain stage in a few hours and stand about twothirds through the 2016 TDP, you may feel that you are out of the running for the yellow jersey for the most primes and be thinking what are my chances at that green jersey...interestingly, the green jersey has had an extremely variable set of outcomes across all the previous TDP:
In 2010 and 2013, there was no mega prime found in the TDP, and the yellow jersey winner took home the green jersey as well (i.e., the "brute force" approach).
On the other hand, in 2009, there was no mega prime found, but the yellow jersey winner was beat out for the green jersey by another cruncher (i.e., the "crunch for midsized" primes approach).
Finding a mega prime won the day in both 2011 and 2012, but not just any mega prime would do in either of those years. In 2011, a 321 mega prime beat out a GFN18 mega prime; in 2012, a GFN18 mega prime beat out both a 121 mega prime and a 27 mega prime (i.e., the "go big or go home" approach).
In 2014, we had yet another result where the yellow jersey winner beat out an SR5 mega prime find (i.e., "brute force" beat "go big or go home").
2015 offered yet another result pattern where a single cruncher found TWO PPS mega primes and still lost the green jersey, but this time it was to someone other than the yellow jersey winner (i.e., "crunch for midsized" beat "go big or go home")!
So what will it be this year? A repeat of one of these former patterns? Or will it be something new yet again? No matter what, the bottom line is this: despite the recent find of a GFN18 mega prime, the green jersey is most definitely still in play!!!
Hmm... crunch GFN19 since it's extremely unlikely that there's going to be a 2nd prime so close to the previous one, or keep at GFN18 due to the smaller chance at GFN19...... Inb4 CUL, PSP, WOO and GFN20 race for the 11th known prime number. Or SoB findings.  


Hmm... crunch GFN19 since it's extremely unlikely that there's going to be a 2nd prime so close to the previous one, or keep at GFN18 due to the smaller chance at GFN19...... Inb4 CUL, PSP, WOO and GFN20 race for the 11th known prime number. Or SoB findings.
I decided to participate by looking to also acquire Gold badges for CUL and 321. The former will complete at the end of this week and 321 starts next Monday.
Lots of time remaining ....  

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Apologies to those who know the correct terms to describe probability. Do primes obey the coin toss argument? Say you just had 10 heads in a row, the 11th toss will still be 50% either way as the coin has no memory of the past. Assuming so, the next GFN18 test still has near enough the same chance of being prime as the one that was prime. Well, the chance might decrease a tiny amount since as numbers get bigger the chances goes down, but the difference will be small. On the plus side, any further GFN18 prime found would almost certainly be bigger, unless you got an old resend where no successful previous result was returned. So given the longer time required to process bigger numbers, plus they also have a lower chance anyway, I'd say the best odds to get the red jersey is still to do GFN18, at least for GPU.
It is more complicated by the CPU app still using a faster transform for 19. Does the speed advantage outweigh the lower chances from being bigger numbers? I'll have to leave that for someone else to work out.
Or just be lucky. That can alter even the best plans.  

Michael GoetzVolunteer moderator Project administrator Project scientist
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Hmm... crunch GFN19 since it's extremely unlikely that there's going to be a 2nd prime so close to the previous one, or keep at GFN18 due to the smaller chance at GFN19...... Inb4 CUL, PSP, WOO and GFN20 race for the 11th known prime number. Or SoB findings.
Intuitive, but incorrect. Primes don't have an even distribution. You'll get huge gaps where no primes are found (like the last 3 years of GFN18 with no primes), and then you'll get something like this and this.
GFN18 is statistically more likely to find another prime before GFN19 does, both because they're more common and because you'll be able to perform more tests because the tests are shorter.
Since "prime score" is meant to reflect the difficulty of finding a prime, you can use it as a rough estimate of the relative likelihood of finding a prime over a given period of time. Assume that the prime score for a GFN18 is about 5,000, and the prime score for a GFN19 is about 30,000. That means that over a given period of time, you're about 6 times more likely to find a GFN18 than a GFN19. And it doesn't matter at all how recently a prime has been found in either project.
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Apologies to those who know the correct terms to describe probability. Do primes obey the coin toss argument? Say you just had 10 heads in a row, the 11th toss will still be 50% either way as the coin has no memory of the past. Assuming so, the next GFN18 test still has near enough the same chance of being prime as the one that was prime. Well, the chance might decrease a tiny amount since as numbers get bigger the chances goes down, but the difference will be small.
Yes, your "coin toss argument" above describes exactly how everybody thinks GFN primes behave. I.e. the chance of a prime is "stochastically independent" of the primality of nearby numbers.
Now, of course it is not in reality "random" if a number is prime or not, so thinking of this as a random process which "has no memory" is useful, but we do not know with absolute certainty how good that model is.
For generalized Fermat primes GF(n, b) = b^(2^n)+1 it has not even been mathematically proved that there are infinitely many of them (with n>0). So we cannot know with mathematical certainty that the conjectured primality "probability" will keep working.
For arbitrary whole numbers x we know that the "probability" x is prime should be taken as 1/(log x). And here we have the prime number theorem (proved in 1896) which says that you can approximate the true number of primes in a huge area well by taking the sum of all these little probabilities 1/(log x).
/JeppeSN  


Now, of course it is not in reality "random" if a number is prime or not, so thinking of this as a random process which "has no memory" is useful, but we do not know with absolute certainty how good that model is.
Cramér's random model is strong. Granville showed that it should be corrected by applying a sieve to remove the correlations.
The numbers are sieved first then we can apply the random model to the sieve output.
It is true that if the likehood of finding a prime is 1/1000 and b^N+1 is prime then the likehood of the next candidates is still 1/1000, the prime doesn't create "a repulsive force".
"All models are wrong but some are useful", George Box.
 

Michael GoetzVolunteer moderator Project administrator Project scientist
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Mountain Stage Preliminary Results
It will probably be a few more days until the Mountain Stage Results are finalized. There's three primes from February 19th still in the pipeline waiting for wingmen.
However, those three primes will each be the first Mountain Stage prime for their respective discovers, so nobody else is going to find two primes.
Therefore, the winner of the 2016 polkadot jersey is Orange_1050 with two primes found and a tie breaking prime score of 163.76390422636496.
Second place goes to 288larsson, also with two primes, with a prime score of 130.00111060588148.
Third place will be decided once the other three primes are in.
Congratulations!!!
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Congratulations to Orange_1050 and 288larsson! GG guys! :)
Beautiful jersey Orange_1050!
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Thank you very much.
Me and my team crunching@EVGA always try to participate in all your challenges.
This mountain stage really took me with surprise.
Thanks again
Orange
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Michael GoetzVolunteer moderator Project administrator Project scientist
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We have now surpassed the previous record for the highest cumulative prime score!
Congratulations everyone. This is the real measure of how well we're doing as a whole. While we won't come close to matching the 766 primes found in 2011  and probably never will again  that's merely a reflection of how much easier it is to find the much smaller primes that were being crunched at that time.
The prime score, on the other hand, incorporates both the computing time required to find a prime of a given size as well as the likelihood of that number being prime. It's a much better metric of primefinding prowess.
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I'm excited to hear that we have surpassed the previous record for highest cumulative prime score about 3/4 of the way through the month. I'm looking forward to seeing what other primes are found in the remaining seven days.
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GFN16
Excluding a couple of primes in the pipeline, PrimeGrid has found 90 GFN16 (b^65536+1) primes, all time, dating back to 2011.
Amazingly, 36 of those 90 primes have been found during the first 22 days of this year's TDP!
At the beginning of the month, b was at about 6.3M. The first prime found was 6379668^65536+1. Since then, b has increased by almost 50%. The most recent (released) prime found was 9373148^65536+1.
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Michael GoetzVolunteer moderator Project administrator Project scientist
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The Mountage Stage results are now final!
With two PPSE primes, Orange_1050 takes the 2016 polkadot jersey for the most primes during the Fenruary 19th Mountain Stage, edging out 288larsson who had two smaller SGS primes. Congratulations!
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JimBVolunteer moderator Project administrator Project developer Send message
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Currently there are three users with primes who haven't given PrimeGrid permission to report them. Emails were sent to all three. If you know any of these users, please let them know about this.
User Andrey Razuvaev from Russia, no team affiliation, has a reportable GFN prime.
User ken wong from Hong Kong, member of Team China, has 3 SGS primes.
User Owner, country unknown, no team affiliation, has an SGS prime.
In the case of the first two, the fact that their usernames appear to be their real names doesn't matter. They still need to enter their real names and grant permission for us to report primes in PrimeGrid Preferences. While it doesn't matter which venue is used, the default venue is probably best. It's only necessary to enter it once (in a single venue). And for everyone else out there who has never granted permission, please take the time to do so now. 19 days after the prime notification email, we'll report the prime in the name of the doublechecker. If that person doesn't respond after another 19 days we'll report the prime anonymously.  

Michael GoetzVolunteer moderator Project administrator Project scientist
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It will be a little while before they're made public, but we've found two mega primes today.
Think that's amazing? How about this: This is the seventh time we've found two mega primes in a single day!
20110508:
http://www.primegrid.com/download/trp123547.pdf
http://www.primegrid.com/download/trp415267.pdf
20140328:
http://www.primegrid.com/download/mega3496188.pdf
http://www.primegrid.com/download/mega3490971.pdf
20140409:
http://www.primegrid.com/download/SR5104944.pdf
http://www.primegrid.com/download/SR5207394.pdf
20140610:
http://www.primegrid.com/download/mega3570132.pdf
http://www.primegrid.com/download/mega3570777.pdf
20150106:
http://www.primegrid.com/download/ESP161041.pdf
http://www.primegrid.com/download/mega3411847.pdf
20150510:
http://www.primegrid.com/download/mega3486411.pdf
http://www.primegrid.com/download/mega3486379.pdf
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Michael GoetzVolunteer moderator Project administrator Project scientist
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Almost had three mega primes in the same day. They are in the same day if you're in the United States, but going by UTC time (which we do), the third one was found on the 25th. All three were, however, found within a 24 hour span.
When it rains, it pours. And it's pouring right now, both figuratively and literally.
Interesting trivia: The double checker on the second mega prime is the prime finder on the third mega prime.
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Almost had three mega primes in the same day.
Expected number of mega primes in 2016: 50 (pessimistic).
Expected number of mega primes per day: lambda ~ 0.15.
Compute Poisson Distribution:
http://homepage.stat.uiowa.edu/~mbognar/applets/pois.html
P(X=2) ~ 0.01 (each day)
P(X=2) in 2016 ~ 1  (1  0.01)^366 = 97.5%
P(X=3) ~ 0.0005 (each day)
P(X=3) in 2016 ~ 16.7%
 

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Almost had three mega primes in the same day.
Expected number of mega primes in 2016: 50 (pessimistic).
Expected number of mega primes per day: lambda ~ 0.15.
Compute Poisson Distribution:
http://homepage.stat.uiowa.edu/~mbognar/applets/pois.html
P(X=2) ~ 0.01 (each day)
P(X=2) in 2016 ~ 1  (1  0.01)^366 = 97.5%
P(X=3) ~ 0.0005 (each day)
P(X=3) in 2016 ~ 16.7%
I've been wondering if these figures are always off by just a little bit because the theoretical application doesn't match the practical application. That is, the Poisson takes into account only the count process of prime distribution, while the actual process of prime finding (at least in the aggregate) involves both the count distribution of primes and the practical binary distribution of successful work completion vs. failed work units. Thus, would a more accurate estimate in practice be generated with a zeroinflated Poisson (using either a binary logistic or probit to model the zeroinflated process)?
 


I've been wondering if these figures are always off by just a little bit because the theoretical application doesn't match the practical application. That is, the Poisson takes into account only the count process of prime distribution, while the actual process of prime finding (at least in the aggregate) involves both the count distribution of primes and the practical binary distribution of successful work completion vs. failed work units. Thus, would a more accurate estimate in practice be generated with a zeroinflated Poisson (using either a binary logistic or probit to model the zeroinflated process)?
My intention was to show that "three mega primes in the same day" is not unexpected, not to compute actual probability.
If we find more than 183 mega primes this year, we solve your problem :o)  

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I can announce two of the three mega primes now.
The first was a PPSMEGA, found by zunewantan: 189*2^3596375+1
The second was a GFN17MEGA, found by dem0707: 43163894^131072+1
Congratulations!
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Hmm... crunch GFN19 since it's extremely unlikely that there's going to be a 2nd prime so close to the previous one [...]
An experimental result is better than theory:
43163894^131072 + 1 and 43165206^131072 +1 are prime!  

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Hmm... crunch GFN19 since it's extremely unlikely that there's going to be a 2nd prime so close to the previous one [...]
An experimental result is better than theory:
43163894^131072 + 1 and 43165206^131072 +1 are prime!
Sometime in some row of the prime data, once ( I am sure about that) that row of data will become famous because one prime will follow to another :)
It is just question when, not how :)
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9 *10^10095671 REPDIGIT MEGA PRIME :) :) :)
57*2^33399321 MEGA PRIME :)
10994460^131072+1 GENERALIZED FERMAT :)
31*332^367560+1 CRUS PRIME :)
Proud member of team Aggie The Pew. Go Aggie!  

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Hmm... crunch GFN19 since it's extremely unlikely that there's going to be a 2nd prime so close to the previous one [...]
An experimental result is better than theory:
43163894^131072 + 1 and 43165206^131072 +1 are prime!
Sometime in some row of the prime data, once ( I am sure about that) that row of data will become famous because one prime will follow to another :)
It is just question when, not how :)
And it just happened now, (and again with the twin GFN Michael linked), so I'd expect a few years before this was to happen once more.
But hey, SoB findings on the last few seconds of TDP is totally real!  


Hmm... crunch GFN19 since it's extremely unlikely that there's going to be a 2nd prime so close to the previous one [...]
An experimental result is better than theory:
43163894^131072 + 1 and 43165206^131072 +1 are prime!
Sometime in some row of the prime data, once ( I am sure about that) that row of data will become famous because one prime will follow to another :)
It is just question when, not how :)
The smallest known GFN gaps are:
 4096: 125440 125442 (2)
 8192: 6755756 6755760 (4)
 16384: 99712832 99712838 (6)
 32768: 2354572 2354618 (46)
 65536: 2483590 2484264 (674)
 131072: 43163894 43165206 (1312)
 


Hmm... crunch GFN19 since it's extremely unlikely that there's going to be a 2nd prime so close to the previous one [...]
An experimental result is better than theory:
43163894^131072 + 1 and 43165206^131072 +1 are prime!
Sometime in some row of the prime data, once ( I am sure about that) that row of data will become famous because one prime will follow to another :)
It is just question when, not how :)
The smallest known GFN gaps are:
 4096: 125440 125442 (2)
 8192: 6755756 6755760 (4)
 16384: 99712832 99712838 (6)
 32768: 2354572 2354618 (46)
 65536: 2483590 2484264 (674)
 131072: 43163894 43165206 (1312)
This is interesting. If we fix the exponent, say 131072, and consider the complete list of b values in natural order:
62722, 130816, 228188, 386892, 572186, 689186, 909548, 1063730, 1176694, 1361244, ...
and then take the first differences of this:
68094, 97372, 158704, 185294, 117000, 220362, 154182, 112964, 184550, ...
what would you (Yves or others) expect to be the minimum of this sequence of integers? Should it be 2 ("twin" b values)? And what about the lim inf of this sequence (we expect an infinite sequence!), should lim inf be finite (cf. Yìtáng Zhāng's recent result) or even 2 as well?
If we consider b^2 + 1 (or b^(2^1) + 1), the b differences are A214516.
/JeppeSN  

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The smallest known GFN gaps are:
4096: 125440 125442 (2)
8192: 6755756 6755760 (4)
16384: 99712832 99712838 (6)
So my prediction is already proven :)
4096: 125440 125442 (2) is close as can be close: cannot be closer :)
Beauty of primes!
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9 *10^10095671 REPDIGIT MEGA PRIME :) :) :)
57*2^33399321 MEGA PRIME :)
10994460^131072+1 GENERALIZED FERMAT :)
31*332^367560+1 CRUS PRIME :)
Proud member of team Aggie The Pew. Go Aggie!  

Michael GoetzVolunteer moderator Project administrator Project scientist
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I can announce two of the three mega primes now.
The first was a PPSMEGA, found by zunewantan: 189*2^3596375+1
The second was a GFN17MEGA, found by dem0707: 43163894^131072+1
The third mega prime was another GFN17MEGA, found by Freezing: 43165206^131072+1
Congratulations!
That is the sixth mega prime found during the month of February, which breaks our old record of 5 mega primes set in July of 2014.
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That is the sixth mega prime found during the month of February, which breaks our old record of 5 mega primes set in July of 2014.
Awesome!
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Founder of CRUNCHERS SANS FRONTIERES
www.crunchersansfrontieres.org
CSF lucky number 22872882^65536+1  


The smallest known GFN gaps are:
4096: 125440 125442 (2)
8192: 6755756 6755760 (4)
16384: 99712832 99712838 (6)
So my prediction is already proven :)
4096: 125440 125442 (2) is close as can be close: cannot be closer :)
Beauty of primes!
There are easier proofs of that prediction, for example:
F(1)=GF(1,2)=2^2+1=5 and F(2)=GF(2,2)=GF(1,4)=4^2+1=17
or:
GF(1,24)=24^2+1=577 and GF(1,26)=26^2+1=677.
What I wanted to know was if GF(n,b) and GF(n,b+2) can be both prime for larger n. And how often?
Addition: OEIS A118539 gives the smallest A (an odd number) such that GF(n,A1) and GF(n,A+1) are both primes, and it has examples for all n up to 12 (where A=125441 as we know). But can examples be found for n over 12 (so 2^n over 4096)?
/JeppeSN  


Thanks Michael  

Michael GoetzVolunteer moderator Project administrator Project scientist
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We're in the TDP Home Stretch!
Only a day and a half remain in the 2016 edition of the Tour de Primes. With three jerseys up for grabs this year, the race is a bit more interesting.
The yellow jersey (count of primes) currently looks like this:
tng* 47
Scott Brown 42
zunewantan 21
tng* has held a similar lead for most of the month, but Scott is still within striking distance. Both have several primes in the pipeline that haven't shown yet, but Scott has one more than tng*, which narrows the gap to just 4 primes.
For the green jersey (total prime score) the math is simple this year: the jersey will likely go to whomever finds the largest prime. The only possible exception is if Scott or tng* finds a "small" mega prime; that might give them enough to overtake boss's GFN18. I suspect Scott and tng* are going all out to find small primes, however, so I'd be surprised if one of them lands "the big one".
Here's the current standings for the green jersey:
boss 5345.66374822409
tng* 3923.8933983897987
Scott Brown 3726.500029864189
Finally, the very firstever red jersey (largest prime), as previously stated, will go to boss unless someone else finds another GFN18 or even larger mega prime (over 1.6 million digits). Here's the current standings:
boss 1,612,400 5135.9255 (GFN18 1415198^262144+1)
zunewantan 1,082,620 1513.6939 (PPSMEGA 189*2^3596375+1)
1998golfer 1,079,358 1499.7461 (PPSMEGA 275*2^3585539+1)
Of course, primes, large or small, can (and do!) come unexpectedly, so anything is possible during the last 18 hours. Stay tuned...
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Of course, primes, large or small, can (and do!) come unexpectedly, so anything is possible during the last 18 hours
Isn't one and a half days actually 36 hours
.
____________
Largest Primes to Date:
As Double Checker: SR5 109208*5^1816285+1 Dgts1,269,534
As Initial Finder: SR5 243944*5^12585761 Dgts879,713
 

Michael GoetzVolunteer moderator Project administrator Project scientist
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Of course, primes, large or small, can (and do!) come unexpectedly, so anything is possible during the last 18 hours
Isn't one and a half days actually 36 hours
.
::thinks quickly::
Of course, but I don't expect anything unusual to happen during the first half of those 36 hours!
Now, if you'll excuse me, I need to go make a 90 second egg.
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Thanks Michael!
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CSF lucky number 22872882^65536+1  

Michael GoetzVolunteer moderator Project administrator Project scientist
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YUUUUUGE NEWS!
As it turns out, it's a good thing this is a leap year because we've found a rather significant prime during "overtime".
A Sophie Germain pair, and a new world record for Sophie Germain primes, has been found. This is the first Sophie Germain pair we've found since 2012, and only the third pair we've ever found.
2618163402417*2^12900001
2618163402417*2^12900011
These SGS primes were found at 05:39:14 UTC today by Scott Brown. Congratulations Scott!!!
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YUUUUUGE NEWS!
As it turns out, it's a good thing this is a leap year because we've found a rather significant prime during "overtime".
A Sophie Germain pair, and a new world record for Sophie Germain primes, has been found. This is the first Sophie Germain pair we've found since 2012, and only the third pair we've ever found.
2618163402417*2^12900001
2618163402417*2^12900011
These SGS primes were found at 05:39:14 UTC today by Scott Brown. Congratulations Scott!!!
Is now exponent 1290000 over, or it will be searched forward?
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9 *10^10095671 REPDIGIT MEGA PRIME :) :) :)
57*2^33399321 MEGA PRIME :)
10994460^131072+1 GENERALIZED FERMAT :)
31*332^367560+1 CRUS PRIME :)
Proud member of team Aggie The Pew. Go Aggie!  


Awesome! Congrats Scott!
Thanks for sharing this news, Michael!
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Founder of CRUNCHERS SANS FRONTIERES
www.crunchersansfrontieres.org
CSF lucky number 22872882^65536+1  


Congrats Scott! I originally read the news wrong and thought my Twin Prime was beat, but I see that the SGS was found first. Nice job!
I guess I am still a record holder, for now.
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My lucky numbers are 121*2^45538991 and 3756801695685*2^666669±1  

Michael GoetzVolunteer moderator Project administrator Project scientist
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Is now exponent 1290000 over, or it will be searched forward?
That's a really good question, and we haven't even started to talk about it yet. For the near future we stay at this exponent because we would need to do new sieving if we wanted to use a different exponent.
We did search 666666 until we found both an SGS pair and a twin prime, but we found the twin first.
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"course, but I don't expect anything unusual to happen during the first half of those 36 hours!"
"These SGS primes were found at 05:39:14 UTC today by Scott Brown. Congratulations Scott!!!"
By my calculations, these primes were found in the uneventful first half.
:)
____________
1437 · 2^495800 + 1  

Michael GoetzVolunteer moderator Project administrator Project scientist
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RULE CLARIFICATIONS
A) In the event that the Yellow Jersey (count of primes) ends in a tie, the tiebreaker will be the prime score. (This is the same as the rule for ties in the Mountain Stage Polka dot Jersey.)
B) With an SGS or TWIN, both primes count towards the prime counts (yellow) and prime score (green).
I'll be updating the first post to reflect these clarifications.
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YUUUUUGE NEWS!
As it turns out, it's a good thing this is a leap year because we've found a rather significant prime during "overtime".
A Sophie Germain pair, and a new world record for Sophie Germain primes, has been found. This is the first Sophie Germain pair we've found since 2012, and only the third pair we've ever found.
2618163402417*2^12900001
2618163402417*2^12900011
These SGS primes were found at 05:39:14 UTC today by Scott Brown. Congratulations Scott!!!
Really cool. I can see that PrimeGrid has been finding lots and lots of "lonely" primes of the form k*2^12900001 ever since July 2012, and now finally a prime with a matching prime is found.
And they are still large enough in their own rights to be included in the top 5000 for general primes.
/JeppeSN  


Congratulations Scott, you found the largest known composite Mersenne number!
 

Michael GoetzVolunteer moderator Project administrator Project scientist
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After 29 days, more than 300 primes, 6 mega primes, and one SGS pair, the 2016 Tour de Primes is officially over.
There's still about 20 primes in the pipeline (including a few that are probably incorrectly reported as prime by faulty computers), so the yellow, green, and red jerseys are still up for grabs.
Stay tuned for the official results!
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There's still about 20 primes in the pipeline (including a few that are probably incorrectly reported as prime by faulty computers), so the yellow, green, and red jerseys are still up for grabs.
Please don't me that this is my inconclusive Woodwall being reported as prime, as it's most likely wrong on my end....  

Michael GoetzVolunteer moderator Project administrator Project scientist
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There's still about 20 primes in the pipeline (including a few that are probably incorrectly reported as prime by faulty computers), so the yellow, green, and red jerseys are still up for grabs.
Please don't me that this is my inconclusive Woodwall being reported as prime, as it's most likely wrong on my end....
It's not yours. :)
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Is now exponent 1290000 over, or it will be searched forward?
That's a really good question, and we haven't even started to talk about it yet. For the near future we stay at this exponent because we would need to do new sieving if we wanted to use a different exponent.
We did search 666666 until we found both an SGS pair and a twin prime, but we found the twin first.
This has been discussed and we have a plan for moving forward, which you can discuss in over in the SGS topic. The short answer is we're continuing to search n=1290000.
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Michael GoetzVolunteer moderator Project administrator Project scientist
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Preliminary Results
It will be a few days before all the primes from February have worked their way through the full process and show up on the leaderboard. Since the race for the yellow jersey is so close, with Scott Brown leading tng* with 51 vs. 50 primes, we needed to be certain that no more primes would affect the battle for first place. Right now, between the two of them there's only one more prime in the pipeline, and that prime was found by Scott Brown, so he's going to finish with either 51 or 52 primes while tng* is going to finish with 50.
Scott Brown is therefore the winner of the 2016 Tour de Primes yellow Jersey! Congratulations Scott!
This is one of the closest TDP races I can remember. Tng* and Scott were neck and neck for almost the entire month.
The red and green jerseys are a little murkier. Whomever wins the red jersey (largest prime) will also win the green jersey (cumulative prime score). Both will almost certainly go to boss with the 1,612,400 digit GFN prime 1415198^262144+1.
The uncertainty is due to there currently being three inconclusive primes being checked by third computers right now, two Woodalls and a TRP. They're almost certainly not prime, but need to be checked since all of them are larger than boss's GFN. In case the triplecheck wingmen take an unusually long time to return those tasks I'm also running them on one of the servers. Worst case is we'll know definitively who won the red and green jerseys by early next week.
(Woodall, TRP, SGS, and the "1" form of 321 use an algorithm that is likely to produce false primes when there's a computation error. On the other hand, the algorithms used for "+1" numbers, or when the base is not 2, just produce bad residues when there's a calculation error.)
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Congratulations to Scott Brown, tng*, zunewantan, boss, 1998golfer, Orange_1050, 288larsson, stream and all the volunteers for this awesome TDP 2016!
Thanks so much Michael for keeping us informed of the progress of this TDP :)
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Michael GoetzVolunteer moderator Project administrator Project scientist
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Official Winners
Although we're still waiting for 4 primes to make their way through the process, they won't affect the winners so I can now officially announce the winners of the 2016 Tour de Primes.
Largest Prime:
The brandnewfor2106 firstever red jersey goes to boss for the 1,612,400 digit mega prime 1415198^262144+1.
Most Primes:
The 2016 yellow jersey goes to Scott Brown. Scott found 52 primes. (At this moment, the TDP results page shows Scott having 51 primes. One of the 4 primes still hidden will eventually bring Scott's total to 52.)
Highest Prime Score:
The 2106 green jersey also goes to boss with a total score of 5345.66374822409.
Mountain Stage (most primes on February 19th):
The 2016 polkadot jersey goes to Orange_1050. Orange_1050 found 2 primes during the Mountain Stage, and won the tiebreaker with a prime score of 163.76390422636496.
Congratulations to boss, Scott, and Orange_1050!
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pschoeferVolunteer developer Volunteer tester
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If you are interested in the distribution of the primes among the different projects, have a look at this histogram:
A similar plot depicting the race for the yellow jersey:
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Thanks for this histogram of primes pschoefer! Really interesting!
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Founder of CRUNCHERS SANS FRONTIERES
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CSF lucky number 22872882^65536+1  

Michael GoetzVolunteer moderator Project administrator Project scientist
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All the primes are now fully processed and reported, so once again here are the final results:
Official Winners
Largest Prime:
The brandnewfor2016 firstever red jersey goes to boss for the 1,612,400 digit mega prime 1415198^262144+1.
Most Primes:
The 2016 yellow jersey goes to Scott Brown. Scott found 52 primes. (At this moment, the TDP results page shows Scott having 51 primes. One of the 4 primes still hidden will eventually bring Scott's total to 52.)
Highest Prime Score:
The 2016 green jersey also goes to boss with a total score of 5345.66374822409.
Mountain Stage (most primes on February 19th):
The 2016 polkadot jersey goes to Orange_1050. Orange_1050 found 2 primes during the Mountain Stage, and won the tiebreaker with a prime score of 163.76390422636496.
Congratulations to boss, Scott, and Orange_1050!
This was quite the Tour de Primes. We set a record for total prime score, with 43656.50. That obliterated the prior record from last year of 30268.46.
The 346 primes found this year are the most since 2012  and the primes were a lot smaller and much easier to find back then.
Well done everyone, and I hope to see you in next year's TDP!
And, of course, we have the "From Pi to Paddy" SR5 challenge starting next week. See you there!
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Please do not PM me with support questions. They will usually go unanswered. Ask on the forums instead. Thank you!
 

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