Newbie questions about the project

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David703

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Message 813 - Posted: 30 Apr 2018, 13:58:24 UTC
Last modified: 30 Apr 2018, 14:57:58 UTC

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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Sergei Chernykh
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Message 814 - Posted: 30 Apr 2018, 16:22:51 UTC - in response to Message 813.  
Last modified: 30 Apr 2018, 16:23:15 UTC

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.
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David703

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Message 815 - Posted: 30 Apr 2018, 20:33:52 UTC - in response to Message 814.  

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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Sergei Chernykh
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Message 816 - Posted: 30 Apr 2018, 21:36:09 UTC - in response to Message 815.  

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.
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David703

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Message 817 - Posted: 1 May 2018, 6:20:52 UTC - in response to Message 816.  

Ok, thanks for the infos!
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David703

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Message 821 - Posted: 3 May 2018, 20:53:34 UTC - in response to Message 816.  

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.
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Sergei Chernykh
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Message 822 - Posted: 3 May 2018, 22:02:54 UTC - in response to Message 821.  

/task_size parameter is how many numbers to check in this work unit. It's used to calculate WU progress.
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David703

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Message 823 - Posted: 4 May 2018, 12:22:57 UTC - in response to Message 822.  

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?
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Sergei Chernykh
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Message 824 - Posted: 4 May 2018, 12:34:14 UTC - in response to Message 823.  

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".
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David703

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Message 825 - Posted: 4 May 2018, 14:48:46 UTC - in response to Message 824.  

Thanks for linking the article, I'll read it!
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David703

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Message 829 - Posted: 8 May 2018, 14:04:37 UTC

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.
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Sergei Chernykh
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Message 830 - Posted: 8 May 2018, 15:11:47 UTC - in response to Message 829.  

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.
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David703

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Message 831 - Posted: 10 May 2018, 17:04:49 UTC - in response to Message 830.  

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.
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Sergei Chernykh
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Message 832 - Posted: 10 May 2018, 18:57:47 UTC - in response to Message 831.  

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.
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David703

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Message 833 - Posted: 10 May 2018, 19:14:11 UTC - in response to Message 832.  

Ok thanks!
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Scott_Cox

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Message 837 - Posted: 14 May 2018, 8:35:10 UTC

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?
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Sergei Chernykh
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Message 838 - Posted: 14 May 2018, 9:10:32 UTC - in response to Message 837.  

Yes, Feb 2019, and yes, it's still an open question.
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SoNic1967

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Message 894 - Posted: 9 Sep 2018, 0:35:44 UTC

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?
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SoNic1967

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Message 895 - Posted: 9 Sep 2018, 0:54:31 UTC - in response to Message 894.  

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>
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