Part 2 of the 10²¹ search will be finished, for the most part, today. There are still ~2000 unfinished WUs which can take up to a couple of weeks to complete, depending on individual participants processing them.

Part 3 of the search will look for amicable pairs where the smaller member of the pair has its largest prime factor between 10¹¹ and 10¹⁴:

m=m1*p, 10¹¹ < p < 10¹⁴

There are too many primes larger than 10¹⁴ (all primes up to 5*10¹⁹ need to be checked), so they will require a different approach and a new application when the time comes.

Most of the participants have already started getting part 3 WUs. The new work units will require ~2.5-2.7 GB RAM on CPU, and the same amount of RAM on GPU (for GPU applications), so the minimum requirement for GPUs will be 3 GB RAM.

Update April 9th, 2024: I found a bug in OpenCL applications, which resulted in many false negatives (around 12.5%). The bug was in the new code that I added for the part 3, so the previous search is unaffected. Version 3.09 has this bug fixed, but I had to restart the part 3. Luckily, we were only a couple of weeks in.

Très bonne nouvelle.
On est prêt pour manger toute cette nouvelle aventure.
Merci pour ton travail :)

It is interesting how many other searches do you expect?

Thanks for the update, Sergei. I greatly appreciate the timely updates and explanations! I am delighted to be crunching on behalf of such a well-managed enterprise.

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I found a bug in OpenCL applications, which resulted in many false negatives (around 12.5%). The bug was in the new code that I added for the part 3, so the previous search is unaffected. Version 3.09 has this bug fixed, but I had to restart the part 3. Luckily, we were only a couple of weeks in.

Good catch! Will all Part 3 WU's run on 3.08 need to be re-run? And if so, will the false-negative tasks and/or their earned credit be removed?

All old v3.08 WUs need to be re-run (each WU missed ~12.5% of amicable pairs), but earned credit will remain.

At the time of this post there is 17.0919% remaining of part 3 at the current speed (eqv) 9,743.98 x Intel Core i9-14900KF it is expected to be completed in November (2025)

Part 3 completes when the largest prime factor in M reaches 10¹⁴. Currently it's at ~3*10¹³. As for P_max > 10¹⁴, all amicable pairs in that range should already be known thanks to a few exhaustive searches I did on my own, using a different approach. But to double check it, I will run the regular search in the range 10¹⁴...10¹⁵ - this will be part 4 of the search.

Appreciate the feedback. Look forward to hearing more about part 4 when the time comes.

Looks like a couple of pairs were found yesterday/today (2025/2025-09-19). https://sech.me/ap/log/2025/2025-09-19/VOLUNTEERS%40BOINC.txt

I'm not seeing the new larger WU. Consistently I'm seeing the same 1276MiB.

There is no larger WUs, at least in terms of used GPU memory,

How many more parts are there to 10^21? When is it estimated that 10^22 will begin.

There will be one more part for 10²¹, several months worth of tasks - it will check largest prime factors > 10¹⁴ to confirm that all amicable numbers are already found in that range.

As for 10²² - I'm not sure it's feasible. The current search took 6 years, so 10²² should take more than 60 years (the scaling is a bit worse than linear)...

At the time of posting providing there is no downtime between the end of part 3 & beginning of part 4. Part 4 will start around 2025-11-02

In late-2019, had you estimated how long 10^21 would take to complete, you probably would have estimated much longer than 6 years. More people are getting GPUs and GPUs are getting faster. However, 10^22 is still going to take a long, long time.

What are your plans for Amicable Numbers after 10^21?

It would be fun to search for Amicable Pairs for 10^22, 10^23, etc. for those factors which are likely to produce many pairs, without running 10^22, 10^23, etc. for all possibilities. Based on the runs beyond 10^21 that you, Chesnut, Costello and others have done, you should have a good idea which factors are likely to produce the most Amicable Pairs.

I estimated that 10²¹ would take 40 years, and it took 6 years only: https://sech.me/boinc/Amicable/forum_thread.php?id=77&postid=614#614

But it's mostly thanks to the other exhaustive searches I did for largest prime factors > 10¹⁴. If not for them, the current search would have to continue up until 5*10¹⁹, and that's at least another 6 years.

There will be one more part for 10²¹, several months worth of tasks - it will check largest prime factors > 10¹⁴ to confirm that all amicable numbers are already found in that range.

As for 10²² - I'm not sure it's feasible. The current search took 6 years, so 10²² should take more than 60 years (the scaling is a bit worse than linear)...

If I maintain a "avg work done" of a "4,200,000" am I in with a chance of being able to reach the top "credit badge" (currently 368,529,287 before the end the project?. I gather finding her amicable pairs should be reasonably low while working on part 4?

Top credit badge is given for 1 billion credits, so probably not... Part 4 shouldn't find any new amicable pairs, that's the whole point of it - it will double check the exhaustive searches I did before in that range.

Top credit badge is given for 1 billion credits, so probably not... Part 4 shouldn't find any new amicable pairs, that's the whole point of it - it will double check the exhaustive searches I did before in that range.

Thank you for the feedback. From what you have said it sounds like the double check part of the project will be reasonably short. For example not lasting into February 2026