As you can see from the title, I would like to ask some quesitons about the project:
1)Do you go through all the numbers in your serach for amicable pairs (odd numbers included)?
2)Why in some periods of time the number of amicable pairs found is high and in others it is much lower?
3)In the list of the amicable pairs found by me I see the numbers and the list of their prime factors, why are these factors so important here?
4)Is there a way to see the computing time you've put into the project? If there is not, are you planning to add it?

Thank you in advance and congratulations for your project!

Edit: I realized after posting that the thread should have actually been posted in Random Stuff, I apologize.

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1) Not through all numbers, only through numbers that can't be proven to not be amicable. ~2.5% of all numbers need to be checked.
2) Distribution of amicable numbers is not uniform and heavily depends on their factorization.
3) Factorization is provided for convenience. It allows to check the numbers quickly.
4) I don't track it, although I save all completed work units and I know how much CPU time each work unit takes on average.

Thank you for the answer.
But so, regarding to the first answer, are you actually going to find all the amicable pairs under the number 10^20 after the end of the current search or are you going to miss some?

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All the amicable pairs under 10²⁰. I meant that it's only needed to check ~2.5% of all numbers below 10²⁰ to do that.

Ok, thanks for the infos!

Hey, I have another question: when I go to a workunit's page, I can see in the command line section a number after the words task size. I would like to know what exactly is that number.

Thanks in advance.

/task_size parameter is how many numbers to check in this work unit. It's used to calculate WU progress.

Ok thanks.
I'm sorry to bother you, but I have another question: how do you decide wheter to test a number or not? How can you prove without the test that a number can't be part of an amicable pair?

There is no short answer to these questions, it's better to read the article describing the algorithm: https://sech.me/ap/articles.html#a1 - especially part 3, "Reducing search space".

Thanks for linking the article, I'll read it!

I would like to ask another question. In the readme on github I've seen that there are mainly two types of searches that you can perform with the program: from to and largest prime factor. I know it's stupid, but I can't figure out what it means to have a factorization between a certain factorization and another, could you define it? Also, how can you spot all the numbers with largest prime factor between two certain numbers when you perform the second type of search?

Thank you for your patience.

what it means to have a factorization between a certain factorization and another, could you define it?

Factorization order is defined as follows: take two factorizations A and B in normalized form (all factors ordered from smallest to largest), compare respective factors one by one until there is a difference. If n-th factor from A is less than n-th factor from B then factorization of A precedes factorization of B. If n-th factor matches, but its power is less than in B (for example, 17² and 17³) then again factorization of A precedes factorization of B.

Example: 3^7*5^2*13*311*32189 precedes 3^7*5^2*13*487*1399 because 311 < 487

Also, how can you spot all the numbers with largest prime factor between two certain numbers when you perform the second type of search?

The second part of the search goes through all numbers of the form N*p < 10²⁰ where p is a prime number between numbers in the command line and N goes through all amicable candidates which are < 10²⁰/p. All these candidates are calculated when a work unit starts to execute, it takes a few seconds to do.

Now I perfectly understand, thank you! When are WUs rich in amicable pairs going to start? Because I see that in the last period there are often less than 100 amicable pairs discovered per day.

When are WUs rich in amicable pairs going to start?

They're already finished. Next time will be in 2019 when the project starts the search up to 10²¹.

Ok thanks!

https://sech.me/boinc/Amicable/server_status.php - so Feb 2019 is projected date for a list of all proved amicable pairs below 10^20? What do you know about the question as to whether there are infinitely many amicable pairs, this is an open question isn't it?

Yes, Feb 2019, and yes, it's still an open question.

I have just started to use Amicable numbers and I have decided to add another video card that I had laying around. Same brand as the first one, weaker performance, but with 2GB of memory.
Now... How do I "tell" Boinc/Amicable to use the second card too?

Got it. I had to create the file cc_config.xml in the Program Data/Boinc directory, file containing the following:

<cc_config>
<options>
<use_all_gpus>1</use_all_gpus>
</options>
</cc_config>