When we started the AP 27 search, we decided to search both shift 0 and shift 640 equally.

With an AP27 challenge starting in a few weeks, I decided to look into whether it was time to also start searching shift 1280.

The higher the shift, the fewer AP sequences you'll find. But as k increases within a shift, the number of sequences you find also decreases. There comes a point where you should start searching the next shift.

Right now, for every million k we search, we're finding about 1400 APs at shift 0 and about 1050 APs at shift 640.

If we started shift 1280, we'd probably get something between 700 and 1000 APs per million k. Definitely less than either 0 or 640.

Rather than open up 1280, we've closed down 640 and will run only shift 0 for a while until it's producing about 1050 APs per million k.

Both shift 0 and shift 640 are currently at approximately k=74M.
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My lucky number is 75898⁵²⁴²⁸⁸+1

I may have missed it in my thread browsing, but what exactly are "shifts"?

Also, will this affect task size (i.e. runtime) and/or credit?
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Eating more cheese on Thursdays.

I may have missed it in my thread browsing, but what exactly are "shifts"?

Also, will this affect task size (i.e. runtime) and/or credit?

That clears it up a bit, thanks. The paper was an interesting read, will need some digesting, though.
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Eating more cheese on Thursdays.

In the AP27 version of the search, we search 10 shifts at once, effectively creating 640 bit shifts, so the shifts are 0, 640, 1280, 2560, etc.

In the AP27 version of the search, we search 10 shifts at once, effectively creating 640 bit shifts, so the shifts are 0, 640, 1280, 2560, etc.

Wouldn't the next after 1280 be 1920 then?

So here's a somewhat "lazy" question because I haven't done any digging. I'm wondering how the list of ap's found is sorted. I ask because several ap's I've found recently are listed much lower than earlier finds.

Is this because of the change in parameters and we are only doing shift 0 at the moment? Also, is there a size for the ap (not referring to whether it's a 20 or 21 or ....) but with in the same range? (maybe this is the reason for the order)

Cheers

This seems to be "unsorted". It is not sorted by smallest term (the part before the plus, such as 316274648710690823). It is not sorted by the common difference in the progression (the coefficient to n, such as 72225058*23#). And it is also not sorted by the date (such as (2018-10-07 12:11:54 UTC)).

Just a question. Since we've changed the search pool so to speak and limited it to just 0 for now was wondering if your estimate of found APs was holding true.

Asked the wrong question.

Since the change to shift 0 only, is there any change in the distribution of APs found? Ie, more AP20's or more AP22's ? Just curious if the increase in units being worked made any difference what so ever in what AP's were found both in number and/or number (20-27).

Here's some raw data. Feel free to come to your own conclusions. AP20 through AP26 are percentages of total.

In the AP27 version of the search, we search 10 shifts at once, effectively creating 640 bit shifts, so the shifts are 0, 640, 1280, 1920, etc.

Right now, both shift 0 and shift 640 are at k = ~74M. We're freezing shift 640 where it is, and continuing with shift 0 until it reaches k = 143 M. At that point we will resume shift 640 and we will also start shift 1280.

From then on we will follow this pattern:

* All the shifts that have been started (initially, 0, 640, and 1280) will run in parallel until the most recently started shift (1280 initially) reaches k = 70M. Every shift will be approximately 70M k's ahead of the next shift.

* When the most recent shift gets to k = 70M, another shift (the next will be 1920) is started at k=0.

* The process then repeats.

* When a shift reaches k = 318M, it is shut down (the AP27 program will overflow otherwise).

* Shift 9600 is the last shift where k can go up to 318M. Shifts beyond 9600 have lower K limits.

I don't really understand the paper posted by Michael in the earlier post.

Is there a simple explanation of the parameters of the AP search? I found this line in stderr:

"ap27_3.01_opencl_windows64.exe 196376536 196376656 0"

How will this relate to the AP tested? Or is it not as simple as that?

Thanks
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Primes: 1281979 & 12+8+1979 & 1+2+8+1+9+7+9 & 1^2+2^2+8^2+1^2+9^2+7^2+9^2 & 12*8+19*79 & 12^8-1979 & 1281979 + 4 (cousin prime)

"ap27_3.01_opencl_windows64.exe 196376536 196376656 0"

How will this relate to the AP tested? Or is it not as simple as that?

Thanks, that was very helpful.
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Primes: 1281979 & 12+8+1979 & 1+2+8+1+9+7+9 & 1^2+2^2+8^2+1^2+9^2+7^2+9^2 & 12*8+19*79 & 12^8-1979 & 1281979 + 4 (cousin prime)