God's Algorithm out to 13f*

 
Just finished running out to a distance of 13 in the face turn metric.

First, the positions at exactly that distance:

 d   mod M + inv          mod M       positions
-- ------------- -------------- ---------------
 0             1              1               1
 1             2              2              18
 2             8              9             243
 3            48             75            3240
 4           509            934           43239
 5          6198          12077          574908
 6         80178         159131         7618438
 7       1053077        2101575       100803036
 8      13890036       27762103      1332343288
 9     183339529      366611212     17596479795
10    2419418798     4838564147    232248063316
11   31909900767    63818720716   3063288809012
12  420569653153   841134600018  40374425656248
13 5538068321152 11076115427897 531653418284628
Next, the positions at that distance or less:
 d   mod M + inv          mod M       positions
-- ------------- -------------- ---------------
 0             1              1               1
 1             3              3              19
 2            11             12             262
 3            59             87            3502
 4           568           1021           46741
 5          6766          13098          621649
 6         86944         172229         8240087
 7       1140021        2273804       109043123
 8      15030057       30035907      1441386411
 9     198369586      396647119     19037866206
10    2617788384     5235211266    251285929522
11   34527689151    69053931982   3314574738534
12  455097342304   910188532000  43689000394782
13 5993165663456 11986303959897 575342418679410
This was a ten-day computation on a machine without ECC, so I hope to get it verified independently.