Welcome to the Number Theory Week Challenge

The fifth Challenge of the 2017 Challenge series is a 5 day challenge to celebrate Number Theory Week 2017. The challenge is being offered on the 321 Prime Search (LLR) application.

The conference Number Theory Week 2017 is organised on the occasion of the 60th birthday of Jerzy Kaczorowski. Reflecting his broad interests, the conference will be devoted to all areas of Number Theory, with special emphasis on Analytic Number Theory.

The conference will be organised jointly by the Institute of Mathematics of the Polish Academy of Sciences, the Polish Mathematical Society, and the Faculty of Mathematics and Computer Science of Adam Mickiewicz University. It will be held September 4-8, 2017 at the Faculty of Mathematics and Computer Science of Adam Mickiewicz University, Poznań, Poland.

To participate in the Challenge, please select only the 321 Prime Search (LLR) project in your PrimeGrid preferences section. The challenge will begin 3rd September 2017 18:00 UTC and end 8th September 2017 18:00 UTC.

Application builds are available for Linux 32 and 64 bit, Windows 32 and 64 bit and MacIntel. Intel CPUs with AVX capabilities (Sandy Bridge, Ivy Bridge, Haswell, Broadwell, Skylake, Kabylake) will have a very large advantage, and Intel CPUs with FMA3 (Haswell, Broadwell, Skylake, Kabylake) will be the fastest.

ATTENTION: The primality program LLR is CPU intensive; so, it is vital to have a stable system with good cooling. It does not tolerate "even the slightest of errors." Please see this post for more details on how you can "stress test" your computer. Tasks will take ~16 hours on fast/newer computers and 48+ hours on slower/older computers. If your computer is highly overclocked, please consider "stress testing" it. Sieving is an excellent alternative for computers that are not able to LLR. :)

Highly overclocked Haswell, Broadwell, Skylake, or Kabylake (i.e., Intel Core i7, i5, and i3 -4xxx or better) computers running the application will see fastest times. Note that 321 is running the latest FMA3 version of LLR which takes full advantage of the features of these newer CPUs. It's faster than the previous LLR app and draws more power and produces more heat. If you have a Haswell, Broadwell, Skylake, or Kabylake CPU, especially if it's overclocked or has overclocked memory, and haven't run the new FMA3 LLR before, we strongly suggest running it before the challenge while you are monitoring the temperatures.

Please, please, please make sure your machines are up to the task.

Multi-threading is also now available, and can speed up tasks, giving you a greater chance of being the Prime finder. As an example a 321 task using 8 threads on an i7-7820X took less than 4:15.

Time zone converter:

The World Clock - Time Zone Converter

NOTE: The countdown clock on the front page uses the host computer time. Therefore, if your computer time is off, so will the countdown clock. For precise timing, use the UTC Time in the data section to the left of the countdown clock.

Scoring Information

Scores will be kept for individuals and teams. Only tasks issued AFTER 3 September 2017 18:00 UTC and received BEFORE 8th September 2017 18:00 UTC will be considered for credit. We will be using the same scoring method as we currently use for BOINC credits. A quorum of 2 is NOT needed to award Challenge score - i.e. no double checker. Therefore, each returned result will earn a Challenge score. Please note that if the result is eventually declared invalid, the score will be removed.


At the Conclusion of the Challenge

We kindly ask users "moving on" to ABORT their tasks instead of DETACHING, RESETTING, or PAUSING.

ABORTING tasks allows them to be recycled immediately; thus a much faster "clean up" to the end of an LLR Challenge. DETACHING, RESETTING, and PAUSING tasks causes them to remain in limbo until they EXPIRE. Therefore, we must wait until tasks expire to send them out to be completed.

Please consider either completing what's in the queue or ABORTING them. Thank you. :)

About 321 Search

321 Search began in February 2003 from a post by Paul Underwood seeking help from interested parties in a prime search attempt of the form 3*2^n-1. The initial goal was to build upon the completed work at Proth Search and extend the list of known primes to an exponent of 1 million (n=1M). That was quickly achieved so they advanced their goal to finding a mega prime for which they sieved up to n=5M.

As seen on PrimeGrid's front page, that goal was achieved on 23 Mar 2008, 7:57:28 UTC, when Dylan Bennett of Canada returned a positive result for n=4235414 (3*2^4235414-1). official announcement | decimal representation

PrimeGrid added the +1 form and continues the search up to n=25M.

Primes known for 3*2^n+1 occur at the following n (PrimeGrid's finds in bold & linked):
1, 2, 5, 6, 8, 12, 18, 30, 36, 41, 66, 189, 201, 209, 276, 353, 408, 438, 534, 2208, 2816, 3168, 3189, 3912, 20909, 34350, 42294, 42665, 44685, 48150, 54792, 55182, 59973, 80190, 157169, 213321, 303093, 362765, 382449, 709968, 801978, 916773, 1832496, 2145353, 2291610, 2478785, 5082306, 7033641, 10829346

Primes known for 3*2^n-1 occur at the following n (PrimeGrid's finds in bold & linked):
1, 2, 3, 4, 6, 7, 11, 18, 34, 38, 43, 55, 64, 76, 94, 103, 143, 206, 216, 306, 324, 391, 458, 470, 827, 1274, 3276, 4204, 5134, 7559, 12676, 14898, 18123, 18819, 25690, 26459, 41628, 51387, 71783, 80330, 85687, 88171, 97063, 123630, 155930, 164987, 234760, 414840, 584995, 702038, 727699, 992700, 1201046, 1232255, 2312734, 3136255, 4235414, 6090515, 11484018, 11731850, 11895718


What is LLR?

The Lucas-Lehmer-Riesel (LLR) test is a primality test for numbers of the form N = k*2^n − 1, with 2^n > k. Also, LLR is a program developed by Jean Penne that can run the LLR-tests. It includes the Proth test to perform +1 tests and PRP to test non base 2 numbers. See also:

• Lucas-Lehmer-Riesel test (WIKI)
  
• Download LLR by Jean Penné
  

(Edouard Lucas: 1842-1891, Derrick H. Lehmer: 1905-1991, Hans Riesel: 1929-2014).
____________

There are lots of lectures at the Conference. Abstract from two of them below.

RECENT RESULTS ABOUT CLOSE PRIMES AND SOME CONJECTURES OF ERDÖS
János Pintz (MTA Rényi Institute)
Abstract: Over the last 90 years lot of efforts were made by excellent mathematicians (Hardy, Littlewood, Rankin, Erdös, Bombieri, Davenport and others) to understand the behaviour of gaps between consecutive primes. The best result was still in 2004 the assertion that there are infinitely many prime gaps which are smaller than the respective average log x by a factor 0.248... (Helmut Maier, 1988). Twelve years ago in joint work with Goldston and Yildirim we succeeded to show this with an arbitrarily small positive constant c in place of 0.248... Somewhat later we showed that there are infinitely many gaps less than the square-root of the average gap size. Simultaneously we showed that under the very deep unproved Elliott-Halberstam conjecture there are infinitely many gaps of size at most 16. In a joint work with Motohashi we proved that there are infinitely many bounded gaps if the Bombieri-Vinogradov theorem can be improved somewhat for smooth moduli. In 2013 Zhang succeeded in this way to show the existence of infinitely many bounded gaps. Eight months later simultaneously and independently Maynard and Tao showed that for an arbitrary k we have a chain of k consecutive primes in bounded intervals of length C(k). While Zhang's work was able to show strong results about gaps between consecutive primes the Maynard-Tao method made able to study consecutive gaps between primes. This method opened the way to prove a number of old conjectures, many of them stated 60-70 years ago by Erdös. In this lecture we give a survey of such results. To mention just one example: Erdös, Pólya and Turán conjectured 60 years ago that if we consider for an arbitrary k a linear combination (with fixed real coefficients) of k consecutive prime gaps then the expression takes infinitely many positive and negative values as well if and only if the non-zero coefficients are not all of the same sign. Some special cases were proved by Erdös (some in joint work with Turán).


VORONOI, SIERPINSKI, ERATOSTHENES
Harald Helfgott (Göttingen University)
Abstract: We show how to carry out a sieve of Erastosthenes up to N in space O(N^(1/3)) and essentially linear time. This improves over the usual versions, which take space about O(√N) and essentially linear time. The algorithm – which, like the one in (Galway, 2000), is ultimately related to diophantine approximation – can also be used to factorize integers n, and thus to give the values of arithmetical functions such as the Möbius function μ and the Liouville function λ for all integers up to N.

It means the returned results don't match, so one or more are wrong. Further units will be sent until two results match, and declared the correct result.

Most likely there was a computation error. If you look at the other units of systems, see if one has a lot of inclusive or invalid units indicating it is unstable. They might also happen rarely for other reasons.

Q2)What causes this status : Completed, Validation Inconclusive ?
Is it an algorithm exception error not dealt with , an unexpected state due to a rounding-off error? (Or a prime find maybe ?)

Q1)How will these events be dealt with when they occur during the challenge, since
credit can be in status pending for days if not weeks?

http://www.primegrid.com/workunit.php?wuid=537119326

http://www.primegrid.com/workunit.php?wuid=537316728

http://www.primegrid.com/workunit.php?wuid=537316810

Hello!

Let's repeat the last challenge, get at least one prime!
Good Luck every one, the hunting has started!!!

Hans Sveen
Oslo, Norway

New member here, just joined because I saw this challenge. This looks like a fun project. I've been on the Einstein and Seti projects currently. Dedicated two I5s to this task, watching the temps...toasty.

Day 1:

Challenge: Number Theory Week
App: 7 (321-LLR)
(As of 2017-09-04 18:14:35 UTC)

12023 tasks have been sent out. [CPU/GPU/anonymous_platform: 11984 (100%) / 0 (0%) / 39 (0%)]

Of those tasks that have been sent out:

795 (7%) came back with some kind of an error. [788 (7%) / 0 (0%) / 7 (0%)]
3765 (31%) have returned a successful result. [3739 (31%) / 0 (0%) / 26 (0%)]
7463 (62%) are still in progress. [7457 (62%) / 0 (0%) / 6 (0%)]

Of the tasks that have been returned successfully:

2288 (61%) are pending validation. [2272 (60%) / 0 (0%) / 16 (0%)]
1443 (38%) have been successfully validated. [1433 (38%) / 0 (0%) / 10 (0%)]
2 (0%) were invalid. [2 (0%) / 0 (0%) / 0 (0%)]
32 (1%) are inconclusive. [32 (1%) / 0 (0%) / 0 (0%)]

The current leading edge (i.e., latest work unit for which work has actually been sent out to a host) is n=13332878. The leading edge was at n=13270859 at the beginning of the challenge. Since the challenge started, the leading edge has advanced 0.47% as much as it had prior to the challenge!
____________
My lucky number is 75898⁵²⁴²⁸⁸+1

Hello, I have a couple questions.
While running this challenge I had one system freeze and I had to do a hard reset.
I did not lose the task it resumed at 87% or so. But the time reset to zero.
So it will look like the time was maybe a half hour where it should be 2 and a half.
It will not be rejected will it?

Second question, are these 321 tasks different sizes.
Two systems that are the same, the tasks should be very close in time to finish?
Or the tasks vary in size and the dimes will vary.

Day 2:

Challenge: Number Theory Week
App: 7 (321-LLR)
(As of 2017-09-05 18:05:31 UTC)

18665 tasks have been sent out. [CPU/GPU/anonymous_platform: 18591 (100%) / 0 (0%) / 74 (0%)]

Of those tasks that have been sent out:

1059 (6%) came back with some kind of an error. [1047 (6%) / 0 (0%) / 12 (0%)]
9357 (50%) have returned a successful result. [9300 (50%) / 0 (0%) / 57 (0%)]
8249 (44%) are still in progress. [8244 (44%) / 0 (0%) / 5 (0%)]

Of the tasks that have been returned successfully:

3900 (42%) are pending validation. [3868 (41%) / 0 (0%) / 32 (0%)]
5352 (57%) have been successfully validated. [5327 (57%) / 0 (0%) / 25 (0%)]
29 (0%) were invalid. [29 (0%) / 0 (0%) / 0 (0%)]
76 (1%) are inconclusive. [76 (1%) / 0 (0%) / 0 (0%)]

The current leading edge (i.e., latest work unit for which work has actually been sent out to a host) is n=13368432. The leading edge was at n=13270859 at the beginning of the challenge. Since the challenge started, the leading edge has advanced 0.74% as much as it had prior to the challenge!
____________
My lucky number is 75898⁵²⁴²⁸⁸+1

Day 3:

Challenge: Number Theory Week
App: 7 (321-LLR)
(As of 2017-09-06 18:23:15 UTC)

25398 tasks have been sent out. [CPU/GPU/anonymous_platform: 25287 (100%) / 0 (0%) / 111 (0%)]

Of those tasks that have been sent out:

1424 (6%) came back with some kind of an error. [1404 (6%) / 0 (0%) / 20 (0%)]
15531 (61%) have returned a successful result. [15444 (61%) / 0 (0%) / 87 (0%)]
8443 (33%) are still in progress. [8439 (33%) / 0 (0%) / 4 (0%)]

Of the tasks that have been returned successfully:

4724 (30%) are pending validation. [4684 (30%) / 0 (0%) / 40 (0%)]
10644 (69%) have been successfully validated. [10597 (68%) / 0 (0%) / 47 (0%)]
67 (0%) were invalid. [67 (0%) / 0 (0%) / 0 (0%)]
96 (1%) are inconclusive. [96 (1%) / 0 (0%) / 0 (0%)]

The current leading edge (i.e., latest work unit for which work has actually been sent out to a host) is n=13404619. The leading edge was at n=13270859 at the beginning of the challenge. Since the challenge started, the leading edge has advanced 1.01% as much as it had prior to the challenge!


5000 tasks a day is pretty impressive considering how large these tasks are. (Normal is about 250 per day.)
____________
My lucky number is 75898⁵²⁴²⁸⁸+1

With one day to go:


Challenge: Number Theory Week
App: 7 (321-LLR)
(As of 2017-09-07 19:06:33 UTC)

32781 tasks have been sent out. [CPU/GPU/anonymous_platform: 32637 (100%) / 0 (0%) / 144 (0%)]

Of those tasks that have been sent out:

1936 (6%) came back with some kind of an error. [1914 (6%) / 0 (0%) / 22 (0%)]
21927 (67%) have returned a successful result. [21810 (67%) / 0 (0%) / 117 (0%)]
8918 (27%) are still in progress. [8913 (27%) / 0 (0%) / 5 (0%)]

Of the tasks that have been returned successfully:

5187 (24%) are pending validation. [5153 (24%) / 0 (0%) / 34 (0%)]
16492 (75%) have been successfully validated. [16410 (75%) / 0 (0%) / 82 (0%)]
102 (0%) were invalid. [102 (0%) / 0 (0%) / 0 (0%)]
146 (1%) are inconclusive. [145 (1%) / 0 (0%) / 1 (0%)]

The current leading edge (i.e., latest work unit for which work has actually been sent out to a host) is n=13443083. The leading edge was at n=13270859 at the beginning of the challenge. Since the challenge started, the leading edge has advanced 1.30% as much as it had prior to the challenge!
____________
My lucky number is 75898⁵²⁴²⁸⁸+1

With one day remaining in the challenge, it's time for our public service announcement about helping at the end of the challenge...

At the Conclusion of the Challenge

We would prefer users "moving on" to finish those tasks they have downloaded, if not then please ABORT the WU's (and then UPDATE the PrimeGrid project) instead of DETACHING, RESETTING, or PAUSING.

ABORTING WU's allows them to be recycled immediately; thus a much faster "clean up" to the end of a Challenge. DETACHING, RESETTING, and PAUSING WU's causes them to remain in limbo until they EXPIRE. Therefore, we must wait until WU's expire to send them out to be completed. Thank you!
____________
My lucky number is 75898⁵²⁴²⁸⁸+1

We're done! Great challenge, everyone. Here's the final statistics:


Challenge: Number Theory Week
App: 7 (321-LLR)
(As of 2017-09-08 18:04:08 UTC)

38522 tasks have been sent out. [CPU/GPU/anonymous_platform: 38347 (100%) / 0 (0%) / 175 (0%)]

Of those tasks that have been sent out:

4800 (12%) came back with some kind of an error. [4773 (12%) / 0 (0%) / 27 (0%)]
28038 (73%) have returned a successful result. [27893 (72%) / 0 (0%) / 145 (0%)]
5628 (15%) are still in progress. [5625 (15%) / 0 (0%) / 3 (0%)]

Of the tasks that have been returned successfully:

4508 (16%) are pending validation. [4484 (16%) / 0 (0%) / 24 (0%)]
23247 (83%) have been successfully validated. [23127 (82%) / 0 (0%) / 120 (0%)]
148 (1%) were invalid. [148 (1%) / 0 (0%) / 0 (0%)]
135 (0%) are inconclusive. [134 (0%) / 0 (0%) / 1 (0%)]

The current leading edge (i.e., latest work unit for which work has actually been sent out to a host) is n=13461386. The leading edge was at n=13270859 at the beginning of the challenge. Since the challenge started, the leading edge has advanced 1.44% as much as it had prior to the challenge!
____________
My lucky number is 75898⁵²⁴²⁸⁸+1

I expect the cleanup to take about 18 to 36 days.

Cleanup Status:
Sep-8: Number Theory Week: 4639 tasks outstanding; 3841 affecting individual (271) scoring positions; 1737 affecting team (66) scoring positions.

____________
My lucky number is 75898⁵²⁴²⁸⁸+1

Cleanup Status:
Sep-8: Number Theory Week: 4639 tasks outstanding; 3841 affecting individual (271) scoring positions; 1737 affecting team (66) scoring positions.
Sep-9: Number Theory Week: 3086 tasks outstanding; 2251 affecting individual (251) scoring positions; 456 affecting team (52) scoring positions.
Sep-10: Number Theory Week: 2271 tasks outstanding; 1535 affecting individual (231) scoring positions; 293 affecting team (41) scoring positions.
Sep-11: Number Theory Week: 1808 tasks outstanding; 1215 affecting individual (216) scoring positions; 207 affecting team (33) scoring positions.
____________
My lucky number is 75898⁵²⁴²⁸⁸+1

PrimeGrid's homepage says

*** 38 tasks, 35 affecting scoring positions, of Number Theory Week Challenge (321-LLR) cleanup work are currently available! ***

How can I help with that ?
Selecting to crunch for the 321 Prime Search sub-project in my PrimeGrid computing preferences is enough ?
Will the scheduler assign me one of these tasks automatically ?

Cleanup Status:
Sep-8: Number Theory Week: 4639 tasks outstanding; 3841 affecting individual (271) scoring positions; 1737 affecting team (66) scoring positions.
Sep-9: Number Theory Week: 3086 tasks outstanding; 2251 affecting individual (251) scoring positions; 456 affecting team (52) scoring positions.
Sep-10: Number Theory Week: 2271 tasks outstanding; 1535 affecting individual (231) scoring positions; 293 affecting team (41) scoring positions.
Sep-11: Number Theory Week: 1808 tasks outstanding; 1215 affecting individual (216) scoring positions; 207 affecting team (33) scoring positions.
Sep-12: Number Theory Week: 1379 tasks outstanding; 797 affecting individual (184) scoring positions; 153 affecting team (26) scoring positions.
Sep-13: Number Theory Week: 1123 tasks outstanding; 590 affecting individual (165) scoring positions; 126 affecting team (24) scoring positions.
Sep-14: Number Theory Week: 910 tasks outstanding; 425 affecting individual (141) scoring positions; 83 affecting team (22) scoring positions.
Sep-15: Number Theory Week: 387 tasks outstanding; 143 affecting individual (72) scoring positions; 19 affecting team (10) scoring positions.
Sep-16: Number Theory Week: 247 tasks outstanding; 85 affecting individual (48) scoring positions; 13 affecting team (7) scoring positions.
Sep-17: Number Theory Week: 185 tasks outstanding; 51 affecting individual (36) scoring positions; 7 affecting team (5) scoring positions.
Sep-18: Number Theory Week: 150 tasks outstanding; 33 affecting individual (26) scoring positions; 7 affecting team (5) scoring positions.
Sep-19: Number Theory Week: 103 tasks outstanding; 16 affecting individual (13) scoring positions; 6 affecting team (4) scoring positions.
Sep-20: Number Theory Week: 74 tasks outstanding; 9 affecting individual (9) scoring positions; 4 affecting team (4) scoring positions.
Sep-21: Number Theory Week: 50 tasks outstanding; 4 affecting individual (4) scoring positions; 1 affecting team (1) scoring positions.
____________
My lucky number is 75898⁵²⁴²⁸⁸+1

The results are final!

Top 3 individuals:

1: zunewantan
2: Scott Brown
3: xii5ku

Top 3 teams:

1: Aggie The Pew
2: Czech National Team
3: SETI.Germany

Congratulations to the winners, and well done to everyone who participated.
See you at the up-coming TRP-LLR Diwali/Deepavali challenge!

____________