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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.
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Scott BrownVolunteer moderator Project administrator Volunteer tester Project scientist
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Joined: 17 Oct 05 Posts: 2121 ID: 1178 Credit: 8,373,213,010 RAC: 6,914,262

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 6sided die. The probability of obtaining any possible value (1, 2, 3, 4, 5, or 6) is always onesixth on a fair die since any given roll is independent of other rolls. For example, if I roll the die once I have onesixth 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?...onesixth, 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 oneinsixth 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).
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141941*2^42994381 is prime!




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 sgsLLRfindingrate is not normal either.
But this only means there are persons that have worse stats. 



Here's the chart for roadrunner_gs



VatoVolunteer tester
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Joined: 2 Feb 08 Posts: 760 ID: 18447 Credit: 213,447,735 RAC: 293,366

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
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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 


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

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
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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?
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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 



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
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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
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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 GoetzVolunteer moderator Project administrator
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Joined: 21 Jan 10 Posts: 13395 ID: 53948 Credit: 228,742,843 RAC: 188,916

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!
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My lucky number is 75898^{524288}+1 



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



VatoVolunteer tester
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Joined: 2 Feb 08 Posts: 760 ID: 18447 Credit: 213,447,735 RAC: 293,366

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 superlucky and find that the first AP26 found, may actually be a subcompenent of an AP27  unlikely though.
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I was waiting and hoping for an AP23 when bang.... AP25!
I guess, I could accept that....If I had to.
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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:
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Updated sub project ratio chart two weeks later.




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.
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