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God's Algorithm out to 15f*

Submitted by tscheunemann on Sun, 08/15/2010 - 14:17.
Yeah, I know this is kind of late, but as promised (or threatened) I have finished my 15f* calculation and here are the results, first positions at exactly that distance (adding a few minor numbers): 
 d  (mod M + inv)*     mod M + inv       mod M             positions
--- --------------- ---------------- ---------------- -----------------
 0                1                1                1                 1
 1                2                2                2                18
 2                8                8                9               243
 3               48               48               75              3240
 4              517              509              934             43239
 5             6359             6198            12077            574908
 6            81541            80178           159131           7618438
 7          1067047          1053077          2101575         100803036
 8         14034826         13890036         27762103        1332343288
 9        184907170        183339529        366611212       17596479795
10       2437753739       2419418798       4838564147      232248063316
11      32135500721      31909900767      63818720716     3063288809012
12     423434369503     420569653153     841134600018    40374425656248
13    5575030719304    5538068321152   11076115427897   531653418284628
14   73286135656774   72805484795034  145610854487909  6989320578825358
15  957963000510751  951720657137855 1903440582318440 91365146187124313
*The first column is again the number of symmetry reduced positions but only considering the symmetry of the coset which is a fixed edge cube position.

And for completeness sake the number of positions up to that distance: 

 d  (mod M + inv)*     mod M + inv       mod M             positions
--- --------------- ---------------- ---------------- -----------------
 0                1                1                1                 1
 1                3                3                3                19
 2               11               11               12               262
 3               59               59               87              3502
 4              576              568             1021             46741
 5             6935             6766            13098            621649
 6            88476            86944           172229           8240087
 7          1155523          1140021          2273804         109043123
 8         15190349         15030057         30035907        1441386411
 9        200097519        198369586        396647119       19037866206
10       2637851258       2617788384       5235211266      251285929522
11      34773351979      34527689151      69053931982     3314574738534
12     458207721482     455097342304     910188532000    43689000394782
13    6033238440786    5993165663456   11986303959897   575342418679410
14   79319374097560   78798650458490  157597158447806  7564662997504768
15 1037282374608311 1030519307596345 2061037740766246 98929809184629081
My congratulations go to Morley Davidson, John Dethridge, Herbert Kociemba, and Tomas Rokicki for beating me to 15f*.
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Another Congratulations

Submitted by Jerry Bryan on Mon, 08/16/2010 - 07:45.
I had already congratulated Tom privately on the God's Number result, and I was worried about flooding this forum with congratulatory messages. But nevertheless, I think it highly appropriate to offer my public congratulations on the God's Number results by the Davidson, Dethridge, Kociemba, and Rokicki team. It's really an amazing accomplishment.

As far as the God's Algorithm results, we have to add tscheunemann to the list to congratulate and thank. Between Tom and tscheunemann, the God's Algorithm results were extended from 11f* to 15f* in an amazingly short period of time. I do hope that work will continue to extend this to 16f*, 17f*, etc. if possible. I also hope that the God's Number results can be calculated for the quarter turn metric (probably 26q*, but we really don't know for sure), and that the God's Algorithm results can also be extended beyond the current 17q* for the quarter turn metric. I've always been partial to the quarter turn metric myself because the generators are conjugate.
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Thank you!

Submitted by rokicki on Sun, 08/15/2010 - 14:49.
We were highly motivated to get the 15f* result before you, primarily because we really wanted to be able to announce a new quantitative result in conjunction with our 20f* result, in order to help validate our runs. If you had not been generating your results like clockwork, we may not have finished our 20f* runs quite so quickly.

So your 15f* confirmation is extremely important to us, and for this we thank you.
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I join Tom in thanking you. C

Submitted by kociemba on Sun, 08/15/2010 - 15:20.
I join Tom in thanking you. Confirming the 15f* result with a completely independent program at least helps to decrease the mistrust in a computational proof of God's number (though I am sure there will never be a "simple" proof written on a few pages of paper.)
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