## Other

drummers-lowrise

Message boards : AP26 - AP27 Search : AP 26 Found Ratios

 Subscribe SortOldest firstNewest firstHighest rated posts first
Author Message
Astro

Joined: 11 Feb 06
Posts: 84
ID: 2390
Credit: 17,557,799
RAC: 0

Message 21434 - Posted: 28 Feb 2010 | 14:41:05 UTC

I took the project wide AP26 data and put it into MS Excel. Then made up this little historical AP26 ratio chart.

Looking at my own data and the project data, I would think I should be or should have found an AP23 by now since if it was found, then the ratio amount under my AP22 column would show a 4 if that AP23 was found. It appears that a muliplier of 4 is about right for all but the AP25 finds.

But should I be finding the AP23 or do I have to get all the 4's before I get the AP23? I've been watching and it seems like I have to get the previous 4's before the higher AP's are found. So, I would need my AP20 hits to be 64, and my AP21's to be 16. This means I have more crunching to do. I certainly should be finding an AP21 shortly.
____________

Scott Brown
Volunteer moderator
Volunteer tester
Project scientist

Joined: 17 Oct 05
Posts: 2247
ID: 1178
Credit: 9,691,723,821
RAC: 12,071,946

Message 21436 - Posted: 28 Feb 2010 | 17:11:26 UTC

Very Nice Charts! ...and some interesting info to see the project ratios for different AP levels.

However, the logic behind using these values to estimate when one "should" find a particular AP is probably not correct given that whether a particular test is an AP of a particular length is independent of other AP tests.

Consider for example a single 6-sided die. The probability of obtaining any possible value (1, 2, 3, 4, 5, or 6) is always one-sixth on a fair die since any given roll is independent of other rolls. For example, if I roll the die once I have one-sixth probability of getting a '6'. Assuming that I roll a '6' on the first roll, what is my chance of rolling another '6' on the second roll?...one-sixth, because the rolls are independent. To put it more in line with the process of obtaining higher AP numbers, consider the case where one is rolling the die 5 times. On each of the first 5 rolls, we happen to get the values '1', '2', '3', '4', and '5'. While it appears like we should get a '6' on the sixth roll, in fact, we still have a one-in-sixth probability of obtaining a '6'. Similarly, whether one has obtained an AP21 or not is irrelevant to the probability of obtaining an AP22 in any given test.

Where your data are most interesting, at least in my opinion, is in showing the stability (or lack thereof) in the ratios across time. In the chart, it is fairly clear that the lower ratios are fairly stable across time (i.e., AP20 divided by AP21), but that the higher AP ratios are not. We also can notice a clear pattern in that variability by taking the difference between the highest and lowest ratio within each AP level across time:

AP20=0.06
AP21=0.09
AP22=0.17
AP23=0.46
AP24=1.10

From this we can see the growth in variability in finds across increasing AP and that this growth is not linear. Indeed, it looks to be very close to exponential. Using that parametric form, one could then forecast when the project on the whole might find an AP26 (though one would of course need to place some sort of confidence bands around such a forecast to get a realistic range).
____________
141941*2^4299438-1 is prime!

Volunteer developer

Joined: 11 Sep 08
Posts: 589
ID: 28785
Credit: 282,855,189
RAC: 278,912

Message 21439 - Posted: 28 Feb 2010 | 20:49:33 UTC

I currently am at:

Found of length 20 66
Found of length 21 10
Found of length 22 5
Found of length 23 0
Found of length 24 0
Found of length 25 1

So this is not "normal" i think, but my sgsLLR-finding-rate is not normal either.
But this only means there are persons that have worse stats.

Astro

Joined: 11 Feb 06
Posts: 84
ID: 2390
Credit: 17,557,799
RAC: 0

Message 21440 - Posted: 28 Feb 2010 | 22:29:42 UTC

Vato
Volunteer tester

Joined: 2 Feb 08
Posts: 793
ID: 18447
Credit: 340,176,174
RAC: 896,143

Message 21444 - Posted: 1 Mar 2010 | 1:47:42 UTC

Here's another data point:

Completed tests 33676
Credit 647,258.67
Found of length 20 65
Found of length 21 19
Found of length 22 2
Found of length 23 2
Found of length 24 2
Found of length 25 1
____________

Maxwell [MM]

Joined: 6 Jul 09
Posts: 12
ID: 42998
Credit: 128,844,376
RAC: 0

Message 21451 - Posted: 1 Mar 2010 | 6:12:34 UTC - in response to Message 21444.

And another data point:

Completed tests 26418
Credit 748,839.18
Found of length 20 48
Found of length 21 16
Found of length 22 8

Lexs
Volunteer developer

Joined: 16 Mar 08
Posts: 61
ID: 20289
Credit: 49,033,000
RAC: 0

Message 21457 - Posted: 1 Mar 2010 | 9:10:15 UTC - in response to Message 21451.

Some more data points from my side.

Completed tests 158577
Credit 2,376,055.35
Found of length 20 180
Found of length 21 60
Found of length 22 13
Found of length 23 3
Found of length 24 1
____________

Vid Vidmar*

Joined: 16 Aug 05
Posts: 45
ID: 377
Credit: 70,953,229
RAC: 0

Message 21458 - Posted: 1 Mar 2010 | 11:23:09 UTC - in response to Message 21457.

Hey, this is fun!

Completed tests 17065
Credit 544,929.45
Found of length 20 36
Found of length 21 7
Found of length 22 3

Is there a stat for finds/tests anywhere?
____________

Uli2*

Joined: 8 Feb 08
Posts: 39
ID: 18752
Credit: 388,430,065
RAC: 600

Message 21480 - Posted: 2 Mar 2010 | 13:02:26 UTC

Points from my side.

Completed tests 29754
Credit 791,081.62
Found of length 20 47
Found of length 21 19
Found of length 22 3
Found of length 23 1
Found of length 24 1

LucasBrown

Joined: 23 Dec 09
Posts: 11
ID: 52589
Credit: 78,125,187
RAC: 24,359

Message 21785 - Posted: 13 Mar 2010 | 22:47:12 UTC

My own data: 66 tests, 2337.06 credits, 2 of length 20.

Adding up all the data so far, we have

Completed tests: 265,556
Credit granted: 5,110,501.33
Found of length 20: 378
Found of length 21: 121
Found of length 22: 29
Found of length 23: 6
Found of length 24: 4
Found of length 25: 1
____________

Astro

Joined: 11 Feb 06
Posts: 84
ID: 2390
Credit: 17,557,799
RAC: 0

Message 21818 - Posted: 15 Mar 2010 | 1:38:50 UTC

OK it's a bit more than a couple weeks later and it seems I did get the AP20 and 21's necesarry to get up to the multiplier of 4 before I snagged my next ap22. Still expecting my AP23 any ole second now.

Come on John, Sending me an ap23 now would help preserve the entire project.....not to mention the ratios.... LOL

____________

Maxwell [MM]

Joined: 6 Jul 09
Posts: 12
ID: 42998
Credit: 128,844,376
RAC: 0

Message 21902 - Posted: 17 Mar 2010 | 5:14:16 UTC - in response to Message 21818.

Come on John, Sending me an ap23 now would help preserve the entire project.....not to mention the ratios.... LOL

I'm with you there... ;-) I'm currently batting about a 2.5 ratio between 20:21:22, anxiously waiting my first AP23...

AP20 = 55
AP21 = 22
AP22 = 9

Michael Goetz
Volunteer moderator

Joined: 21 Jan 10
Posts: 13618
ID: 53948
Credit: 264,850,369
RAC: 303,451

Message 21906 - Posted: 17 Mar 2010 | 12:05:14 UTC - in response to Message 21902.

Come on John, Sending me an ap23 now would help preserve the entire project.....not to mention the ratios.... LOL

I'm with you there... ;-) I'm currently batting about a 2.5 ratio between 20:21:22, anxiously waiting my first AP23...

AP20 = 55
AP21 = 22
AP22 = 9

I seem to be having a bit more luck:

Found of length 20 10
Found of length 21 2
Found of length 22 1
Found of length 23 1

On the other side of the coin, I have yet to find a prime in any of the LLRs.

What is it they say about a watched pot?

Of course the important thing to remember is that even when you don't find anything, you're contributing to the cause. Every negative result brings us, collectively, one step closer to the big prize. And it also helps keep you warm in the winter!
____________
My lucky number is 75898524288+1

DaveSun

Joined: 5 Sep 07
Posts: 44
ID: 11850
Credit: 1,053,134,490
RAC: 787,314

Message 21908 - Posted: 17 Mar 2010 | 12:42:15 UTC

I was waiting and hoping for an AP23 when bang.... AP25!

Found of length 20 13
Found of length 21 3
Found of length 22 1
Found of length 25 1

Vato
Volunteer tester

Joined: 2 Feb 08
Posts: 793
ID: 18447
Credit: 340,176,174
RAC: 896,143

Message 21909 - Posted: 17 Mar 2010 | 13:58:44 UTC - in response to Message 21908.

Don't forget that (although it's not accounted for in the stats), an AP25 also contains 2x AP24, 3x AP23, 4x AP22, etc by shifting the shorter progressions starting point up to the next prime. I don't know if that would make any noticeable difference to these ratios.

Also, like DaveSun found, we might be super-lucky and find that the first AP26 found, may actually be a subcompenent of an AP27 - unlikely though.
____________

Astro

Joined: 11 Feb 06
Posts: 84
ID: 2390
Credit: 17,557,799
RAC: 0

Message 21927 - Posted: 18 Mar 2010 | 1:15:07 UTC - in response to Message 21908.

I was waiting and hoping for an AP23 when bang.... AP25!

I guess, I could accept that....If I had to.
____________

Astro

Joined: 11 Feb 06
Posts: 84
ID: 2390
Credit: 17,557,799
RAC: 0

Message 22107 - Posted: 25 Mar 2010 | 13:24:38 UTC

I've been trying to update my excel sheet each time a new AP was found. I didn't catch each and every change, and sometimes total would advance by more than one between times I looked at them, even if it was less than 12 hours between checking. I created a chart which shows the ratio of one AP to the next lower AP. The Primegrid average is around 4 until you get up to AP 25/26. In other words the average participant should get 4 AP20's for each AP21, and 4 AP 21's for each AP22, and so on.

Here's how mine have tracked:

____________

Astro

Joined: 11 Feb 06
Posts: 84
ID: 2390
Credit: 17,557,799
RAC: 0

Message 22182 - Posted: 29 Mar 2010 | 4:18:56 UTC

Updated sub project ratio chart two weeks later.

Astro

Joined: 11 Feb 06
Posts: 84
ID: 2390
Credit: 17,557,799
RAC: 0

Message 22451 - Posted: 12 Apr 2010 | 14:54:07 UTC

Updated sub project ratio chart and my ratio graph after 2 weeks.

Come on now, the truth of math is clearly in question, as I should have atleast one AP23 if not two to keep the math honest.

____________

Message boards : AP26 - AP27 Search : AP 26 Found Ratios