Welcome to Riemann's 196th Birthday Challenge

The sixth challenge of the 2022 Series will be a 3-day challenge celebrating the 196th birthday of the German mathematician Bernhard Riemann. The challenge will be offered on the WW application, beginning 17 September 20:00 UTC and ending 20 September 20:00 UTC.

Bernhard Riemann was one of the most influential mathematicians from the past few centuries. His name pops up everywhere from precalculus textbooks to unsolvable* math hypotheses about prime numbers to The Simpsons!

Physicists were still far removed from such a way of thinking: space was still, for them, a rigid, homogeneous something, susceptible of no change or conditions. Only the genius of Riemann, solitary and uncomprehended, had already won its way by the middle of the last century to a new conception of space, in which space was deprived of its rigidity, and in which its power to take part in physical events was recognized as possible.
(Albert Einstein)

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. :)

What is the Wieferich and Wall-Sun-Sun Prime Search?

A Wall–Sun–Sun (or Fibonacci–Wieferich) prime is a prime p > 5 in which p^2 divides the Fibonacci number , where the Legendre symbol is defined as

They are named after Donald Dines Wall and twin brothers Zhi-Hong Sun and Zhi-Wei Sun. Drawing on Wall's work, in 1992 the brothers proved that if the first case of Fermat's last theorem was false for a certain prime p, then that p would have to be a Wall–Sun–Sun prime.

A prime p is a Wieferich prime if p^2 divides 2^(p-1) - 1. They are named after Arthur Wieferich who in 1909 proved that if the first case of Fermat’s last theorem is false for the exponent p, then p satisfies the criteria a^(p-1) = 1 (mod p^2) for a=2.

Notice the similarity in the expression p^2 divides 2^(p-1) - 1 to the special case of Fermat's little theorem p divides 2^(p-1) - 1.

For more info about the mathematics and the ranges we're searching, see these forum threads:
https://www.primegrid.com/forum_thread.php?id=9436
WW by the Numbers
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Time flies like an arrow. Fruit flies like a banana.

Exposed 😭
One of these days I'll do one with no mistakes the first time!! ;-)
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Time flies like an arrow. Fruit flies like a banana.

Here is a pre-challenge update on the status of the overall WW project:

The leading edge is currently 15327.169P.
This means the project is 83.09% complete.
In the last month, the project has averaged 18930 tasks per day, which means the project has about 110 more days before it will be completed at the current monthly rate.
In the last day, the project completed 33880 tasks, which means the project has about 61 more days before it will be completed at the current rate.
There is about 24.96 billion credit left to be claimed for the project.

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No Riemann-specific reason. We just mix up the challenge start times over the year, given that there are crunchers in various time zones.
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Time flies like an arrow. Fruit flies like a banana.

A post challenge update on the progress of the WW project:

The leading edge is currently 15950.572P.
This means the project is 86.47% complete.
In the last month, the project has averaged 28270 tasks per day, which means the project has about 59 more days before it will be completed at the current monthly rate. It will probably be longer since the average rate for the last month includes the challenge, which skewed the average by a lot.
In the last day, the project completed 134490 tasks, which means the project has about 12 more days before it will be completed at the rate that tasks were completed during the challenge.
There is about 19.97 billion credit left to be claimed for the project.

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Great challenge everyone! Here are the final stats. Cleanup tasks are available now.

Challenge: Riemann's Birthday
App: 33 (WW)
(As of 2022-09-21 04:11:21 UTC)

407787 tasks have been sent out. [CPU/GPU/anonymous_platform: 7871 (2%) / 398935 (98%) / 981 (0%)]

Of those tasks that have been sent out:

4102 (1%) were aborted. [3495 (1%) / 607 (0%) / 0 (0%)]
5348 (1%) came back with some kind of an error. [2 (0%) / 5346 (1%) / 0 (0%)]
383347 (94%) have returned a successful result. [1732 (0%) / 380636 (93%) / 979 (0%)]
6000 (1%) are still in progress. [1427 (0%) / 4573 (1%) / 0 (0%)]

Of the tasks that have been returned successfully:

5889 (2%) are pending validation. [44 (0%) / 5831 (2%) / 14 (0%)]
376987 (98%) have been successfully validated. [1688 (0%) / 374334 (98%) / 965 (0%)]
494 (0%) were invalid. [0 (0%) / 494 (0%) / 0 (0%)]
8 (0%) are inconclusive. [0 (0%) / 8 (0%) / 0 (0%)]
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Time flies like an arrow. Fruit flies like a banana.

Cleanup Status:

Sep 21: Riemann's Birthday: 4240 tasks outstanding; 1273 affecting individual (137) scoring positions; 170 affecting team (7) scoring positions.
Sep 29: Riemann's Birthday: 30 tasks outstanding; 1 affecting individual (1) scoring positions; 1 affecting team (1) scoring positions.
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Time flies like an arrow. Fruit flies like a banana.

The results are final! (sorry for the delay in posting!)
During the 3 day challenge, we completed 382878 tasks (including doublechecks).

93 teams and 425 individuals participated in the challenge.

Top Three Individuals:
1. [TA]Skillz with 28,521 tasks completed
2. Nick with 24,095 tasks completed
3. vaughan with 21,389 tasks completed

Top Three Teams:
1. TeAm AnandTech with 72,611 tasks completed
2. Antarctic Crunchers with 42,288 tasks completed
3. AMD Users with 33,757 tasks completed

Great work everyone, see you in the next challenge!
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Time flies like an arrow. Fruit flies like a banana.