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
  
• Polk-a-dot Jersey - on the 19th of February we'll have a "mountain" stage and award the Polk-a-dot 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 GFN-16 (65536) projects. Of course, should someone find a prime in the mega-prime 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), GFN-16, 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]x-RaY99_the_one_man_team
- [DPC]x-RaY99_the_one_man_team
- Lonnie Christensen

- [DPC]x-RaY99_the_one_man_team
- [DPC]x-RaY99_the_one_man_team
- PBT_marian_boss

- Scott Brown
- Usucapio Libertatis
- Scott Brown

- shanky123
- [BOINCstats] LostBoy
- Snf*

- lennart
- lennart
- [SG]marodeur6

- lennart
- s-yama
- 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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My lucky number is 75898⁵²⁴²⁸⁸+1

Of course, should someone find a prime in the mega-prime searches, this would almost guarantee the green jersey.

Currently, the fastest opportunities to find Top 5000 primes is with the SGS (LLR), PPSE (LLR), and GFN-16 (65536) projects.

Currently, the fastest opportunities to find Top 5000 primes is with the SGS (LLR), PPSE (LLR), and GFN-16 (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?

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 GFN-16 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 GFN-15 instead.

In both cases, you should leave one CPU core free to feed the GPU.


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My lucky number is 75898⁵²⁴²⁸⁸+1

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*(kmax-kmin)/[(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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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*(kmax-kmin)/[(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.

For GFN numbers, I can give you somewhat better answers because I have all the data.

For GFN-15, since the double check ended, we've seen about 1 prime for every 8800 candidates.

For GFN-16, since the double check ended, the ratio is 1 prime per 16,500 candidates.

For GFN-17-Low, the ratio is about 1 prime per 17,800 candidates.

For larger GFN numbers there are too few primes to give reliable estimates.

Need some recommendation for the set-up of my computers for the 'Tour de Primes.

Have HT turn off...will have the video cards for the GFN-16 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?

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...

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!
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My lucky number is 75898⁵²⁴²⁸⁸+1

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!

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/nj-14sen-results.png?w=400&h=566

I approve of adding a new jersey.
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I didn't say all of it; just a majority of it. And I'll stand by that assessment...

Who is going to New Jersey? I don't live to far from there. Gas is cheap any way.

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.

May I have a recommendation please on my Core-i7 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.

The 2016 Tour de Primes has officially started! Good luck everyone!
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My lucky number is 75898⁵²⁴²⁸⁸+1

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 GFN-16, GFN-17-Low, and GFN-17-Mega. GFN-15, which isn't eligible for TDP, is flat.
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My lucky number is 75898⁵²⁴²⁸⁸+1

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 behind-the-scenes 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^(n-1)-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 GFN-18 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 GFN-15 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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My lucky number is 75898⁵²⁴²⁸⁸+1

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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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?

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.

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.

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.

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 Dgts-1,269,534
As Initial Finder: SR5 243944*5^1258576-1 Dgts-879,713

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?

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?

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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My lucky number is 75898⁵²⁴²⁸⁸+1

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.

I got my annual prime reported today. Now once again trying to find a big one. 8)
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There's a GFN-17-Low 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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My lucky number is 75898⁵²⁴²⁸⁸+1

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 Free-DC.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.

Bok's numbers, while correct per se, are completely useless for your purpose. You can't use them to see how many TDP-eligible primes you have. The ONLY authoritative source is PrimeGrid's TDP leaderboard page.

There's two reasons Free-DC (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 Free-DC 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) Free-DC'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, Free-DC 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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My lucky number is 75898⁵²⁴²⁸⁸+1

The red jersey will be changing hands shortly...
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My lucky number is 75898⁵²⁴²⁸⁸+1

The effect of challenges on the number of primes found each day:

What effect does the Tour de Primes have?

We're almost half way through TDP, and so far 25 GFN-16 primes have been found in the first two weeks of February.

In the previous five years PrimeGrid had discovered only 54 GFN-16 primes. Slightly less than one third of all the GFN-16 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 GFN-16 primes as compared to the 25 discovered in the just the first half of February.
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My lucky number is 75898⁵²⁴²⁸⁸+1

I think you write GFN-15 a couple of places where you mean GFN-16. /JeppeSN

I sense a disturbance in the Force...

Expect the red and green jerseys to change ownership soon.
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My lucky number is 75898⁵²⁴²⁸⁸+1

I sense a disturbance in the Force...

Expect the red and green jerseys to change ownership soon.

The number of GFN-18 primes has changed...

http://www.primegrid.com/stats_genefer.php

The number of GFN-18 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!

So, as we approach the mountain stage in a few hours and stand about two-thirds 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 mid-sized" 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 mid-sized" 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!!!

So, as we approach the mountain stage in a few hours and stand about two-thirds 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 mid-sized" 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 mid-sized" 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!!!

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.

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.

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.

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 polka-dot 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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My lucky number is 75898⁵²⁴²⁸⁸+1