• Welcome to the Speedsolving.com, home of the web's largest puzzle community!
    You are currently viewing our forum as a guest which gives you limited access to join discussions and access our other features.

    Registration is fast, simple and absolutely free so please, join our community of 30,000+ people from around the world today!

    If you are already a member, simply login to hide this message and begin participating in the community!

World record formula for nxnxn cubes

Joined
Feb 8, 2012
Messages
31
Likes
0
Thread starter #1
Not really accurate, but here it is :)

y=7.5(x-2)^2

where x is the n of the nxnxn cube and y is the estimate average world record

the 7.5 is the value of skill that humans have, the lower this number, the more skill we have, if this number goes down a bit then the time for a 3x3x3 cube would also change a bit and the time of a 7x7x7 cube would change alot more :)

if the value of 7.5 becomes 0 then we can solve all cubes in no time :eek:

I just discovered that 7.5 is what it gives for 3x3x3 haha :p if you change that to the exact wr 7.64 than thats what the formula gives ofcourse :D
 
Last edited:
Joined
Feb 8, 2012
Messages
31
Likes
0
Thread starter #3
2x2 solves can get lower but they are almost zero (and yes, 2.12=0 thats about the accuracy of this formula)
 
Joined
May 17, 2009
Messages
4,970
Likes
11
Location
Ponyville
WCA
2009WHIT01
YouTube
ben1996123
#4
Single WR estimate:

Code:
x	y	WR - y
2	0.43571	0.254287
3	6.63572	-0.97572
4	23.8381	2.9319
5	57.2429	-2.3829
6	112.05	2.76
7	193.46	-0.35
8	306.672
9	456.886
10	649.303
11	889.122
\( y=0.866667x^3-2.29881x^2+1.22738x+0.242857 \)
 
Last edited:

Sa967St

Not A Moderator
Joined
Mar 11, 2008
Messages
3,793
Likes
23
Location
Waterloo, ON, Canada
WCA
2007STRO01
YouTube
Sa967St
#5
Excel gives y = 1.0342e^0.7812x with R² = 0.9525 as the exponential curve of best fit using 3-7 WR averages. Interestingly, the result for 7x7x7 is way under the curve, suggesting it's relatively fast compared to the other WRs. :p
 
Joined
May 17, 2009
Messages
4,970
Likes
11
Location
Ponyville
WCA
2009WHIT01
YouTube
ben1996123
#6
Excel gives y = 1.0342e^0.7812x with R² = 0.9525 as the exponential curve of best fit using 3-7 WR averages. Interestingly, the result for 7x7x7 is way under the curve, suggesting it's relatively fast compared to the other WRs. :p
Wolframalpha gives \( y=2.92575e^{0.606276x} \) with R² = 0.996411 with 3-7 averages. Doesn't really seem that good though :p

Code:
x	y	WR - y
2	9.83653	-7.71653
3	18.0362	-10.3962
4	33.0709	0.4991
5	60.6386	-2.6986
6	111.186	9.244
7	203.87	-3.4
8	373.814
9	685.422
10	1256.78
11	2304.43
 
Joined
Jun 6, 2010
Messages
229
Likes
0
Location
Philippines
WCA
2010BULA01
YouTube
TheBloodyTalon
#10
Not really accurate, but here it is :)

y=7.5(x-2)^2

the 7.5 is the value of skill that humans have, the lower this number, the more skill we have, if this number goes down a bit then the time for a 3x3x3 cube would also change a bit and the time of a 7x7x7 cube would change alot more :)
the value of my skill is approximately 13.. :(
 
Joined
Feb 9, 2009
Messages
1,910
Likes
10
WCA
2008ANDE02
YouTube
Minxer2011
#12
Without too much hack etc I got this:
2.10(x-1)^1.892*floor(x/2)

Kinda close for 1-5:
1 | 0 (spot on yay! :D)
2 | 2.1 (0.02 off)
3 | 7.79149 (0.15 off)
4 | 33.5709 (spot on)
5 | 57.8558 (0.08 off)
6 | 132.371 (11.94 off)
7 | 186.897 (13.58 off in the other direction than 6x6x6 :D)
 
Joined
Sep 17, 2009
Messages
848
Likes
18
Location
New Orleans, LA
YouTube
4EverTrying
#13
I think this thread is kind of silly, but to play along, I just came up with a formula. I am not sure what the lowest averages for computer cubes are, so I not sure how values for n greater than 7 compare with human records (computer or by hand).

The Potential time (in seconds) for world record averages of 5 for a cube of size n is:

\( P\left( \text{WR Avg}\text{.}\left( n \right) \right)=\frac{3\text{x3 WR Avg}\text{.}}{\frac{3^{2}}{\ln \left( 3 \right)}\left\lfloor \text{log}_{10}\left( {f}'\left( 3 \right) \right) \right\rfloor }\left\lfloor \text{log}_{10}\left( {f}'\left( n \right) \right) \right\rfloor \frac{n^{2}}{\ln \left( n \right)} \)
, where

\( {f}'\left( n \right)=\text{rate of change of number of positions of a cube of size }n. \)

\( {f}'\left( n \right)=\frac{\left( 8!\times 3^{7} \right)\left( 12!\times 2^{10} \right)24!^{\frac{1}{4}\left( \left( n+1 \right)\left( n-3 \right)+3\cos ^{2}\left( \frac{n\pi }{2} \right) \right)}\ln \left( 24!^{4\left( n-1 \right)}4!^{-24\left( n-2 \right)} \right)}{{}} \)
\( \text{ }8\left( 24\times 12!\times 2^{10} \right)^{\cos ^{2}\left( \frac{n\pi }{2} \right)}4!^{\frac{3}{2}\left( \left( n-1 \right)\left( n-3 \right)+\cos ^{2}\left( \frac{n\pi }{2} \right) \right)} \)

Which I first showed in this post.

\( \left\lfloor \text{log}_{10}\left( {f}'\left( n \right) \right) \right\rfloor \) is power of ten of the rate of change for the number of positions for the nxnxn.

So for n = 1 to 1000 (ignore the value for n = 1), if we use the actual derivative (rate of change formula), with Mathematica input:

AccountingForm[(7.64/(3^2/Log[3]*
Floor[Log[
10, ((8! 3^7) (12! 2^10) (Exp[(Log[4008235231]/4 +
Log[6075]/2 + (11/2) Log[2]) ((3 + 1) (3 - 3) +
3 Cos[3 (Pi/2)]^2)] Log[
24!^(4 (3 - 1))/4!^(24 (3 - 2))]))/(8 (24 12! 2^10)^
Cos[3 (Pi/2)]^2 4!^((3/2) ((3 - 1)*(3 - 3) +
Cos[3 (Pi/2)]^2)))]])) (Range[1000]^2/
Log[Range[1000]])*
Floor[Log[
10, ((8! 3^7) (12! 2^10) (Exp[(Log[4008235231]/4 +
Log[6075]/
2 + (11/2) Log[
2]) ((Range[1000] + 1) (Range[1000] - 3) +
3 Cos[Range[1000] (Pi/2)]^2)] Log[
24!^(4 (Range[1000] - 1))/
4!^(24 (Range[1000] - 2))]))/(8 (24 12! 2^10)^
Cos[Range[1000] (Pi/2)]^2 4!^((3/
2) ((Range[1000] - 1)*(Range[1000] - 3) +
Cos[Range[1000] (Pi/2)]^2)))]] // N]
Yields (in seconds, but I included minutes, hours, days, and years)
Code:
n     Seconds      Minutes       Hours        Days          Years
Code:
2    2.05022    0.034170333    0.00057    2.37294E-05    6.5012E-08       
3    7.64    0.127333333    0.002122    8.84259E-05    2.42263E-07       
4    24.0901    0.401501667    0.006692    0.000278821    7.63892E-07       
5    52.427    0.873783333    0.014563    0.000606794    1.66245E-06       
6    105.288    1.7548    0.029247    0.001218611    3.33866E-06       
7    181.161    3.01935    0.050323    0.002096771    5.74458E-06       
8    299.332    4.988866667    0.083148    0.003464491    9.49176E-06       
9    456.763    7.612716667    0.126879    0.005286609    1.44839E-05       
10    678.896    11.31493333    0.188582    0.007857593    2.15277E-05       
11    956.883    15.94805    0.265801    0.011075035    3.03426E-05       
12    1325.37    22.0895    0.368158    0.015339931    4.20272E-05       
13    1773.2    29.55333333    0.492556    0.020523148    5.62278E-05       
14    2341.76    39.02933333    0.650489    0.027103704    7.42567E-05       
15    3010.87    50.18116667    0.836353    0.034848032    9.54741E-05       
16    3833.91    63.8985    1.064975    0.044373958    0.000121572       
17    4788.17    79.80283333    1.330047    0.055418634    0.000151832       
18    5933.95    98.89916667    1.648319    0.068679977    0.000188164       
19    7236.12    120.602    2.010033    0.083751389    0.000229456       
20    8770.03    146.1671667    2.436119    0.101504977    0.000278096       
21    10498.2    174.97    2.916167    0.121506944    0.000332896       
22    12502.8    208.38    3.473    0.144708333    0.000396461       
23    14730.2    245.5033333    4.091722    0.170488426    0.000467092       
24    17281    288.0166667    4.800278    0.200011574    0.000547977       
25    20099.9    334.9983333    5.583306    0.232637731    0.000637364       
26    23293.6    388.2266667    6.470444    0.269601852    0.000738635       
27    26786.9    446.4483333    7.440806    0.310033565    0.000849407       
28    30708.6    511.81    8.530167    0.355423611    0.000973763       
29    34982.6    583.0433333    9.717389    0.404891204    0.001109291       
30    39743    662.3833333    11.03972    0.459988426    0.001260242       
31    44889.9    748.165    12.46942    0.519559028    0.001423449       
32    50596.2    843.27    14.0545    0.585604167    0.001604395       
33    56736.8    945.6133333    15.76022    0.656675926    0.001799112       
34    63473.7    1057.895    17.63158    0.734649306    0.002012738       
35    70722.9    1178.715    19.64525    0.818552083    0.002242608       
36    78634.4    1310.573333    21.84289    0.91012037    0.00249348       
37    87097.2    1451.62    24.19367    1.008069444    0.002761834       
38    96307.7    1605.128333    26.75214    1.114672454    0.003053897       
39    106108    1768.466667    29.47444    1.228101852    0.003364663       
40    116747    1945.783333    32.42972    1.351238426    0.003702023       
41    128013    2133.55    35.55917    1.481631944    0.004059266       
42    140196    2336.6    38.94333    1.622638889    0.004445586       
43    153105    2551.75    42.52917    1.772048611    0.004854928       
44    166969    2782.816667    46.38028    1.932511574    0.005294552       
45    181623    3027.05    50.45083    2.102118056    0.005759228       
46    197335    3288.916667    54.81528    2.283969907    0.006257452       
47    213877    3564.616667    59.41028    2.475428241    0.006781995       
48    231588    3859.8    64.33    2.680416667    0.007343607       
49    250197    4169.95    69.49917    2.895798611    0.007933695       
50    270037    4500.616667    75.01028    3.125428241    0.008562817       
51    290842    4847.366667    80.78944    3.366226852    0.009222539       
52    312969    5216.15    86.93583    3.622326389    0.009924182       
53    336162    5602.7    93.37833    3.890763889    0.010659627       
54    360772    6012.866667    100.2144    4.175601852    0.011440005       
55    386523    6442.05    107.3675    4.473645833    0.012256564       
56    413755    6895.916667    114.9319    4.788831019    0.013120085       
57    442204    7370.066667    122.8344    5.118101852    0.014022197       
58    472268    7871.133333    131.1856    5.466064815    0.01497552       
59    503629    8393.816667    139.8969    5.829039352    0.015969971       
60    536670    8944.5    149.075    6.211458333    0.017017694       
61    571089    9518.15    158.6358    6.609826389    0.018109113       
62    607331    10122.18333    168.7031    7.029293981    0.01925834       
63    645037    10750.61667    179.1769    7.465706019    0.020453989       
64    684631    11410.51667    190.1753    7.923969907    0.021709507       
65    725775    12096.25    201.6042    8.400173611    0.023014174       
66    768961    12816.01667    213.6003    8.900011574    0.024383593       
67    813785    13563.08333    226.0514    9.41880787    0.025804953       
68    860720    14345.33333    239.0889    9.962037037    0.027293252       
69    909382    15156.36667    252.6061    10.52525463    0.028836314       
70    960318    16005.3    266.755    11.11479167    0.030451484       
71    1013076    16884.6    281.41    11.72541667    0.032124429       
72    1068176    17802.93333    296.7156    12.36314815    0.033871639       
73    1125192    18753.2    312.5533    13.02305556    0.035679604       
74    1184782    19746.36667    329.1061    13.71275463    0.037569191       
75    1246273    20771.21667    346.1869    14.42445602    0.039519058       
76    1310464    21841.06667    364.0178    15.16740741    0.041554541       
77    1376710    22945.16667    382.4194    15.93414352    0.043655188       
78    1445727    24095.45    401.5908    16.73295139    0.045843702       
79    1516896    25281.6    421.36    17.55666667    0.048100457       
80    1591031    26517.18333    441.9531    18.41471065    0.050451262       
81    1667420    27790.33333    463.1722    19.29884259    0.052873541       
82    1746845    29114.08333    485.2347    20.21811343    0.055392092       
83    1828696    30478.26667    507.9711    21.16546296    0.05798757       
84    1913650    31894.16667    531.5694    22.14872685    0.060681443       
85    2001209    33353.48333    555.8914    23.1621412    0.063457921       
86    2092009    34866.81667    581.1136    24.21306713    0.06633717       
87    2185378    36422.96667    607.0494    25.29372685    0.069297882       
88    2282276    38037.93333    633.9656    26.41523148    0.072370497       
89    2381854    39697.56667    661.6261    27.56775463    0.075528095       
90    2485031    41417.18333    690.2864    28.76193287    0.078799816       
91    2591079    43184.65    719.7442    29.98934028    0.082162576       
92    2700875    45014.58333    750.2431    31.26012731    0.085644184       
93    2813577    46892.95    781.5492    32.56454861    0.089217941       
94    2930174    48836.23333    813.9372    33.91405093    0.092915208       
95    3049880    50831.33333    847.1889    35.29953704    0.09671106       
96    3173546    52892.43333    881.5406    36.73085648    0.100632484       
97    3300440    55007.33333    916.7889    38.19953704    0.104656266       
98    3431631    57193.85    953.2308    39.71795139    0.108816305       
99    3565988    59433.13333    990.5522    41.27300926    0.113076738       
100    3704803    61746.71667    1029.112    42.87966435    0.117478532       
101    3846999    64116.65    1068.611    44.52545139    0.121987538       
102    3993818    66563.63333    1109.394    46.22474537    0.126643138       
103    4144043    69067.38333    1151.123    47.96346065    0.131406742       
104    4299055    71650.91667    1194.182    49.75758102    0.13632214       
105    4457701    74295.01667    1238.25    51.59376157    0.141352771       
106    4621198    77019.96667    1283.666    53.48608796    0.146537227       
107    4788563    79809.38333    1330.156    55.42318287    0.151844337       
108    4960951    82682.51667    1378.042    57.41841435    0.157310724       
109    5137229    85620.48333    1427.008    59.45866898    0.162900463       
110    5318815    88646.91667    1477.449    61.5603588    0.168658517       
111    5504309    91738.48333    1528.975    63.70728009    0.174540493       
112    5695285    94921.41667    1582.024    65.91765046    0.180596303       
113    5890419    98173.65    1636.228    68.17614583    0.186783961       
114    6091219    101520.3167    1692.005    70.50021991    0.193151287       
115    6296190    104936.5    1748.942    72.87256944    0.199650875       
116    6507007    108450.1167    1807.502    75.31258102    0.206335838       
117    6722257    112037.6167    1867.294    77.80390046    0.213161371       
118    6943540    115725.6667    1928.761    80.3650463    0.220178209       
119    7169398    119489.9667    1991.499    82.97914352    0.227340119       
120    7401214    123353.5667    2055.893    85.66219907    0.234690956       
121    7638011    127300.1833    2121.67    88.40290509    0.24219974       
122    7880951    131349.1833    2189.153    91.21471065    0.249903317       
123    8128887    135481.45    2258.024    94.08434028    0.257765316       
124    8383292    139721.5333    2328.692    97.02884259    0.265832445       
125    8642702    144045.0333    2400.751    100.0312731    0.274058283       
126    8908916    148481.9333    2474.699    103.1124537    0.282499873       
127    9180138    153002.3    2550.038    106.2515972    0.291100266       
128    9458362    157639.3667    2627.323    109.4717824    0.299922692       
129    9742041    162367.35    2706.123    112.7551042    0.308918094       
130    10032622    167210.3667    2786.839    116.1183102    0.318132357       
131    10328813    172146.8833    2869.115    119.5464468    0.327524512       
132    10632258    177204.3    2953.405    123.0585417    0.337146689       
133    10941313    182355.2167    3039.254    126.6355671    0.346946759       
134    11257985    187633.0833    3127.218    130.3007523    0.356988363       
135    11580260    193004.3333    3216.739    134.030787    0.367207636       
136    11910360    198506    3308.433    137.8513889    0.377675038       
137    12246555    204109.25    3401.821    141.7425347    0.388335712       
138    12590449    209840.8167    3497.347    145.7227894    0.399240519       
139    12940600    215676.6667    3594.611    149.775463    0.410343734       
140    13298831    221647.1833    3694.12    153.9216551    0.421703165       
141    13663309    227721.8167    3795.364    158.1401505    0.433260686       
142    14036259    233937.65    3898.961    162.4567014    0.445086853       
143    14415622    240260.3667    4004.339    166.8474769    0.457116375       
144    14803493    246724.8833    4112.081    171.3367245    0.469415684       
145    15197942    253299.0333    4221.651    175.9021065    0.481923579       
146    15601305    260021.75    4333.696    180.5706597    0.494714136       
147    16011416    266856.9333    4447.616    185.3173148    0.507718671       
148    16430474    273841.2333    4564.021    190.1675231    0.521006913       
149    16856448    280940.8    4682.347    195.0977778    0.53451446       
150    17291789    288196.4833    4803.275    200.1364468    0.548319032       
151    17734220    295570.3333    4926.172    205.2571759    0.562348427       
152    18186046    303100.7667    5051.679    210.4866435    0.576675736       
153    18645135    310752.25    5179.204    215.8001736    0.591233352       
154    19114053    318567.55    5309.459    221.2274653    0.606102645       
155    19590412    326506.8667    5441.781    226.7408796    0.621207889       
156    20076625    334610.4167    5576.84    232.3683449    0.636625602       
157    20570454    342840.9    5714.015    238.0839583    0.652284817       
158    21074587    351243.1167    5854.052    243.918831    0.66827077       
159    21586517    359775.2833    5996.255    249.8439468    0.684503964       
160    22108771    368479.5167    6141.325    255.8885532    0.701064529       
161    22639228    377320.4667    6288.674    262.0281019    0.717885211       
162    23180021    386333.6833    6438.895    268.2872801    0.735033644       
163    23729202    395486.7    6591.445    274.6435417    0.752448059       
164    24289187    404819.7833    6746.996    281.1248495    0.770205067       
165    24857754    414295.9    6904.932    287.7054861    0.788234209       
166    25437129    423952.15    7065.869    294.4112153    0.806606069       
167    26025278    433754.6333    7229.244    301.2184954    0.825256152       
168    26624963    443749.3833    7395.823    308.159294    0.844272038       
169    27233128    453885.4667    7564.758    315.1982407    0.863556824       
170    27853080    464218    7736.967    322.3736111    0.883215373       
171    28481949    474699.15    7911.653    329.6521875    0.903156678       
172    29122608    485376.8    8089.613    337.0672222    0.923471842       
173    29772633    496210.55    8270.176    344.5906597    0.944083999       
174    30434443    507240.7167    8454.012    352.2504977    0.965069857       
175    31105816    518430.2667    8640.504    360.0210185    0.986358955       
176    31789754    529829.2333    8830.487    367.9369676    1.008046487       
177    32482929    541382.15    9023.036    375.9598264    1.030026922       
178    33188929    553148.8167    9219.147    384.1311227    1.052414035       
179    33904631    565077.1833    9417.953    392.4147106    1.075108796       
180    34633150    577219.1667    9620.319    400.8466435    1.098209982       
181    35371849    589530.8167    9825.514    409.3964005    1.121633974       
182    36123631    602060.5167    10034.34    418.097581    1.145472825       
183    36885519    614758.65    10245.98    426.9157292    1.169632135       
184    37660753    627679.2167    10461.32    435.8883449    1.194214644       
185    38446584    640776.4    10679.61    444.9836111    1.219133181       
186    39245739    654095.65    10901.59    454.2330903    1.24447422       
187    40055702    667595.0333    11126.58    463.607662    1.270157978       
188    40879849    681330.8167    11355.51    473.1464005    1.296291508       
189    41714421    695240.35    11587.34    482.8057986    1.322755613       
190    42563453    709390.8833    11823.18    492.6325579    1.349678241       
191    43423421    723723.6833    12062.06    502.5858912    1.376947647       
192    44298133    738302.2167    12305.04    512.7098727    1.404684583       
193    45183681    753061.35    12551.02    522.9592708    1.432765126       
194    46084254    768070.9    12801.18    533.3825694    1.461322108       
195    46996189    783269.8167    13054.5    543.9373727    1.490239377       
196    47923439    798723.9833    13312.07    554.6694329    1.519642282       
197    48861942    814365.7    13572.76    565.5317361    1.549402017       
198    49816046    830267.4333    13837.79    576.5746065    1.579656456       
199    50781945    846365.75    14106.1    587.7539931    1.610284912       
200    51763739    862728.9833    14378.82    599.1173495    1.641417396       
201    52757212    879286.8667    14654.78    610.6158796    1.672920218       
202    53766871    896114.5167    14935.24    622.3017477    1.704936295       
203    54788766    913146.1    15219.1    634.1292361    1.737340373       
204    55827146    930452.4333    15507.54    646.1475231    1.770267187       
205    56877989    947966.4833    15799.44    658.3100579    1.8035892       
206    57944910    965748.5    16095.81    670.6586806    1.837421043       
207    59025225    983753.75    16395.9    683.1623264    1.871677607       
208    60121910    1002031.833    16700.53    695.8554398    1.90645326       
209    61231869    1020531.15    17008.85    708.7021875    1.941649829       
210    62358851    1039314.183    17321.9    721.7459606    1.977386194       
211    63498976    1058316.267    17638.6    734.9418519    2.01353932       
212    64656422    1077607.033    17960.12    748.3382176    2.050241692       
213    65827614    1097126.9    18285.45    761.8936806    2.087379947       
214    67016432    1116940.533    18615.68    775.6531481    2.125077118       
215    68218856    1136980.933    18949.68    789.5700926    2.163205733       
216    69439593    1157326.55    19288.78    803.6989931    2.201915049       
217    70674175    1177902.917    19631.72    817.9881366    2.241063388       
218    71926994    1198783.233    19979.72    832.4883565    2.280790018       
219    73193892    1219898.2    20331.64    847.1515278    2.32096309       
220    74479332    1241322.2    20688.7    862.0293056    2.361724125       
221    75779488    1262991.467    21049.86    877.0774074    2.402951801       
222    77098502    1284975.033    21416.25    892.3437731    2.444777461       
223    78432482    1307208.033    21786.8    907.7833565    2.487077689       
224    79785225    1329753.75    22162.56    923.4401042    2.529972888       
225    81153180    1352553    22542.55    939.2729167    2.573350457       
226    82540623    1375677.05    22927.95    955.3312847    2.617345986       
227    83943110    1399051.833    23317.53    971.5637731    2.661818557       
228    85365827    1422763.783    23712.73    988.0304051    2.706932617       
229    86803836    1446730.6    24112.18    1004.674028    2.752531583       
230    88261975    1471032.917    24517.22    1021.550637    2.798768867       
231    89735650    1495594.167    24926.57    1038.60706    2.845498795       
232    91230214    1520503.567    25341.73    1055.905255    2.892891109       
233    92740568    1545676.133    25761.27    1073.386204    2.94078412       
234    94271702    1571195.033    26186.58    1091.107662    2.98933606       
235    95818873    1596981.217    26616.35    1109.014734    3.038396531       
236    97387601    1623126.683    27052.11    1127.171308    3.08814057       
237    98972168    1649536.133    27492.27    1145.511204    3.138386859       
238    100578626    1676310.433    27938.51    1164.104468    3.189327308       
239    102202094    1703368.233    28389.47    1182.894606    3.240807141       
240    103847337    1730788.95    28846.48    1201.936771    3.292977454       
241    105508917    1758481.95    29308.03    1221.168021    3.345665811       
242    107193544    1786559.067    29775.98    1240.666019    3.399084982       
243    108894764    1814912.733    30248.55    1260.356065    3.453030315       
244    110618907    1843648.45    30727.47    1280.311424    3.50770253       
245    112360376    1872672.933    31211.22    1300.467315    3.56292415       
246    114124631    1902077.183    31701.29    1320.886933    3.618868309       
247    115906471    1931774.517    32196.24    1341.510081    3.675370085       
248    117711932    1961865.533    32697.76    1362.40662    3.732620878       
249    119535246    1992254.1    33204.24    1383.509792    3.790437785       
250    121382035    2023033.917    33717.23    1404.884664    3.84899908       
251    123246938    2054115.633    34235.26    1426.46919    3.908134767       
252    125136170    2085602.833    34760.05    1448.335301    3.96804192       
253    127043789    2117396.483    35289.94    1470.414225    4.028532122       
254    128975579    2149592.983    35826.55    1492.772905    4.089788781       
255    130926544    2182109.067    36368.48    1515.353519    4.151653475       
256    132901511    2215025.183    36917.09    1538.211933    4.214279268       
257    134895928    2248265.467    37471.09    1561.295463    4.277521816       
258    136915756    2281929.267    38032.15    1584.673102    4.341570142       
259    138954253    2315904.217    38598.4    1608.266817    4.406210458       
260    141018522    2350308.7    39171.81    1632.158819    4.471667998       
261    143102268    2385037.8    39750.63    1656.27625    4.537743151       
262    145211609    2420193.483    40336.56    1680.689919    4.604629915       
263    147341251    2455687.517    40928.13    1705.338553    4.67216042       
264    149496299    2491604.983    41526.75    1730.281238    4.740496544       
265    151671931    2527865.517    42131.09    1755.462164    4.809485382       
266    153874446    2564574.1    42742.9    1780.954236    4.879326674       
267    156096713    2601611.883    43360.2    1806.674919    4.949794299       
268    158346232    2639103.867    43985.06    1832.711019    5.021126078       
269    160616349    2676939.15    44615.65    1858.985521    5.093111016       
270    162913520    2715225.333    45253.76    1885.573148    5.165953831       
271    165232151    2753869.183    45897.82    1912.409155    5.239477137       
272    167578212    2792970.2    46549.5    1939.562639    5.313870244       
273    169945441    2832424.017    47207.07    1966.961123    5.388934583       
274    172340469    2872341.15    47872.35    1994.681354    5.464880422       
275    174757546    2912625.767    48543.76    2022.656782    5.541525431       
276    177202802    2953380.033    49223    2050.958356    5.61906399       
277    179669804    2994496.733    49908.28    2079.51162    5.697292111       
278    182165359    3036089.317    50601.49    2108.395359    5.776425641       
279    184683560    3078059.333    51300.99    2137.541204    5.85627727       
280    187230081    3120501.35    52008.36    2167.014826    5.937026922       
281    189800169    3163336.15    52722.27    2196.761215    6.018523877       
282    192398954    3206649.233    53444.15    2226.839745    6.100930809       
283    195020991    3250349.85    54172.5    2257.187396    6.184075057       
284    197672100    3294535    54908.92    2287.871528    6.268141172       
285    200347399    3339123.317    55652.06    2318.835637    6.352974347       
286    203052153    3384202.55    56403.38    2350.14066    6.438741533       
287    205780770    3429679.5    57161.33    2381.721875    6.525265411       
288    208539869    3475664.483    57927.74    2413.655891    6.612755866       
289    211322491    3522041.517    58700.69    2445.862164    6.700992231       
290    214135983    3568933.05    59482.22    2478.425729    6.790207477       
291    216973958    3616232.633    60270.54    2511.272662    6.880199074       
292    219843202    3664053.367    61067.56    2544.481505    6.971182204       
293    222736575    3712276.25    61871.27    2577.969618    7.06293046       
294    225661609    3761026.817    62683.78    2611.824178    7.15568268       
295    228611752    3810195.867    63503.26    2645.969352    7.249231101       
296    231593961    3859899.35    64331.66    2680.48566    7.343796328       
297    234600912    3910015.2    65166.92    2715.288333    7.439146119       
298    237641017    3960683.617    66011.39    2750.474734    7.535547216       
299    240705481    4011758.017    66862.63    2785.943067    7.632720732       
300    243803508    4063391.8    67723.2    2821.799861    7.730958524       
301    246927602    4115460.033    68591    2857.958356    7.830022894       
302    250084267    4168071.117    69467.85    2894.493831    7.930120085       
303    253267318    4221121.967    70352.03    2931.334699    8.03105397       
304    256484053    4274734.217    71245.57    2968.565428    8.133055968       
305    259726779    4328779.65    72146.33    3006.096979    8.235882135       
306    263004322    4383405.367    73056.76    3044.031505    8.339812341       
307    266307446    4438457.433    73974.29    3082.262106    8.444553716       
308    269645804    4494096.733    74901.61    3120.900509    8.550412354       
309    273011528    4550192.133    75836.54    3159.855648    8.657138762       
310    276411436    4606857.267    76780.95    3199.206435    8.764949137       
311    279839033    4663983.883    77733.06    3238.877697    8.873637525       
312    283301972    4721699.533    78694.99    3278.958009    8.983446601       
313    286792179    4779869.65    79664.49    3319.353924    9.094120339       
314    290318903    4838648.383    80644.14    3360.172488    9.205952023       
315    293873224    4897887.067    81631.45    3401.310463    9.318658803       
316    297463728    4957728.8    82628.81    3442.867222    9.432512938       
317    301082149    5018035.817    83633.93    3484.747095    9.547252315       
318    304737953    5078965.883    84649.43    3527.059641    9.663177099       
319    308421222    5140353.7    85672.56    3569.690069    9.779972793       
320    312143092    5202384.867    86706.41    3612.767269    9.897992516       
321    315892753    5264879.217    87747.99    3656.166123    10.01689349       
322    319679873    5327997.883    88799.96    3699.99853    10.13698227       
323    323496695    5391611.583    89860.19    3744.174711    10.25801291       
324    327351411    5455856.85    90930.95    3788.789479    10.38024515       
325    331236176    5520602.933    92010.05    3833.752037    10.50343024       
326    335158458    5585974.3    93099.57    3879.148819    10.62780498       
327    339111128    5651852.133    94197.54    3924.897315    10.75314333       
328    343102561    5718376.017    95306.27    3971.094456    10.87971084       
329    347124732    5785412.2    96423.54    4017.647361    11.00725304       
330    351185276    5853087.933    97551.47    4064.644398    11.13601205       
331    355276901    5921281.683    98688.03    4112.001169    11.26575663       
332    359409011    5990150.183    99835.84    4159.826516    11.39678498       
333    363570869    6059514.483    100991.9    4207.996169    11.52875663       
334    367773660    6129561    102159.4    4256.639583    11.66202626       
335    372007383    6200123.05    103335.4    4305.641007    11.79627673       
336    376281637    6271360.617    104522.7    4355.111539    11.93181244       
337    380587162    6343119.367    105718.7    4404.944005    12.06833974       
338    384934531    6415575.517    106926.3    4455.260775    12.20619391       
339    389313521    6488558.683    108142.6    4505.94353    12.34505077       
340    393733939    6562232.317    109370.5    4557.105775    12.4852213       
341    398187204    6636453.4    110607.6    4608.648194    12.62643341       
342    402681464    6711357.733    111856    4660.665093    12.76894546       
343    407208925    6786815.417    113113.6    4713.066262    12.91251031       
344    411778720    6862978.667    114383    4765.957407    13.05741755       
345    416382081    6939701.35    115661.7    4819.237049    13.20338917       
346    421028237    7017137.283    116952.3    4873.012002    13.35071781       
347    425707411    7095123.517    118252.1    4927.169109    13.49909345       
348    430429835    7173830.583    119563.8    4981.826794    13.64884053       
349    435185626    7253093.767    120884.9    5036.870671    13.79964567       
350    439986051    7333100.85    122218.3    5092.431146    13.95186615       
351    444820203    7413670.05    123561.2    5148.381979    14.10515611       
352    449698529    7494975.483    124916.3    5204.844086    14.25984681       
353    454611879    7576864.65    126281.1    5261.711563    14.41564812       
354    459569872    7659497.867    127658.3    5319.095741    14.57286504       
355    464562310    7742705.167    129045.1    5376.878588    14.73117421       
356    469599855    7826664.25    130444.4    5435.183507    14.89091372       
357    474673163    7911219.383    131853.7    5493.90235    15.05178726       
358    479791085    7996518.083    133275.3    5553.137558    15.2140755       
359    484945137    8082418.95    134707    5612.790938    15.37750942       
360    490146217    8169103.617    136151.7    5672.988623    15.54243458       
361    495381851    8256364.183    137606.1    5733.586238    15.70845545       
362    500664992    8344416.533    139073.6    5794.733704    15.87598275       
363    505984031    8433067.183    140551.1    5856.296655    16.04464837       
364    511351069    8522517.817    142042    5918.41515    16.21483603       
365    516753375    8612556.25    143542.6    5980.94184    16.38614203       
366    522204164    8703402.733    145056.7    6044.029676    16.55898541       
367    527691589    8794859.817    146581    6107.541539    16.73299052       
368    533227993    8887133.217    148118.9    6171.620289    16.90854874       
369    538800387    8980006.45    149666.8    6236.11559    17.08524819       
370    544422248    9073704.133    151228.4    6301.183426    17.26351624       
371    550081490    9168024.833    152800.4    6366.683912    17.44296962       
372    555790701    9263178.35    154386.3    6432.762743    17.62400752       
373    561536630    9358943.833    155982.4    6499.266551    17.80620973       
374    567333020    9455550.333    157592.5    6566.354398    17.99001205       
375    573167543    9552792.383    159213.2    6633.8836    18.17502356       
376    579053034    9650883.9    160848.1    6702.002708    18.36165126       
377    584975976    9749599.6    162493.3    6770.555278    18.54946651       
378    590950385    9849173.083    164152.9    6839.70353    18.73891378       
379    596963684    9949394.733    165823.2    6909.301898    18.92959424       
380    603028959    10050482.65    167508    6979.50184    19.12192285       
381    609133512    10152225.2    169203.8    7050.156389    19.31549696       
382    615288374    10254806.23    170913.4    7121.393218    19.51066635       
383    621485073    10358084.55    172634.7    7193.114271    19.70716239       
384    627732575    10462209.58    174370.2    7265.423322    19.90526937       
385    634021218    10567020.3    176117    7338.208542    20.10468094       
386    640362262    10672704.37    177878.4    7411.600255    20.30575412       
387    646743735    10779062.25    179651    7485.459896    20.5081093       
388    653178106    10886301.77    181438.4    7559.931782    20.71214187       
389    659654417    10994240.28    183237.3    7634.889086    20.91750434       
390    666184138    11103068.97    185051.1    7710.46456    21.12456044       
391    672755066    11212584.43    186876.4    7786.516968    21.3329232       
392    679381051    11323017.52    188717    7863.206609    21.5430318       
393    686048641    11434144.02    190569.1    7940.377789    21.7544597       
394    692770661    11546177.68    192436.3    8018.178947    21.96761355       
395    699534675    11658911.25    194315.2    8096.466146    22.18209903       
396    706353626    11772560.43    196209.3    8175.38919    22.39832655       
397    713216131    11886935.52    198115.6    8254.816331    22.61593515       
398    720134093    12002234.88    200037.2    8334.885336    22.83530229       
399    727096023    12118267.05    201971.1    8415.463229    23.05606364       
400    734112748    12235212.47    203920.2    8496.675324    23.27856253       
401    741173845    12352897.42    205881.6    8578.400984    23.50246845       
402    748291436    12471523.93    207858.7    8660.780509    23.72816578       
403    755452615    12590876.92    209847.9    8743.664525    23.95524528       
404    762672012    12711200.2    211853.3    8827.222361    24.18417085       
405    769935405    12832256.75    213870.9    8911.28941    24.41449153       
406    777256338    12954272.3    215904.5    8996.022431    24.6466368       
407    784621666    13077027.77    217950.5    9081.269282    24.88018981       
408    792046285    13200771.42    220012.9    9167.202373    25.11562294       
409    799515709    13325261.82    222087.7    9253.654039    25.35247682       
410    807043729    13450728.82    224178.8    9340.7839    25.59118877       
411    814616957    13576949.28    226282.5    9428.437002    25.83133425       
412    822250558    13704175.97    228402.9    9516.788866    26.07339415       
413    829929782    13832163.03    230536.1    9605.668773    26.31690075       
414    837668665    13961144.42    232685.7    9695.239178    26.56229912       
415    845453576    14090892.93    234848.2    9785.342315    26.80915703       
416    853299951    14221665.85    237027.8    9876.15684    27.05796395       
417    861192774    14353212.9    239220.2    9967.508958    27.30824372       
418    869146328    14485772.13    241429.5    10059.56398    27.56044926       
419    877146739    14619112.32    243651.9    10152.16133    27.81414063       
420    885209713    14753495.22    245891.6    10245.48279    28.06981586       
421    893319965    14888666.08    248144.4    10339.35145    28.32699027       
422    901492031    15024867.18    250414.5    10433.93554    28.58612478       
423    909711788    15161863.13    252697.7    10529.07162    28.84677156       
424    917995216    15299920.27    254998.7    10624.94463    29.10943734       
425    926326761    15438779.35    257313    10721.37455    29.3736289       
426    934721210    15578686.83    259644.8    10818.53252    29.63981513       
427    943165528    15719425.47    261990.4    10916.26769    29.9075827       
428    951671962    15861199.37    264353.3    11014.72178    30.17731995       
429    960228694    16003811.57    266730.2    11113.75803    30.44865214       
430    968849430    16147490.5    269124.8    11213.53507    30.72201389       
431    977520906    16292015.1    271533.6    11313.89938    30.99698459       
432    986256944    16437615.73    273960.3    11415.01093    31.27400254       
433    995042796    16584046.6    276400.8    11516.69903    31.55260008       
434    1003893759    16731562.65    278859.4    11619.14073    31.83326227       
435    1012794957    16879915.95    281331.9    11722.16385    32.11551741       
436    1021763208    17029386.8    283823.1    11825.96306    32.39989878       
437    1030782131    17179702.18    286328.4    11930.34874    32.68588695       
438    1039867282    17331121.37    288852    12035.50095    32.9739752       
439    1049004938    17483415.63    291390.3    12141.26086    33.26372837       
440    1058209390    17636823.17    293947.1    12247.79387    33.55559963       
441    1067465379    17791089.65    296518.2    12354.92337    33.84910512       
442    1076788722    17946478.7    299108    12462.83243    34.14474639       
443    1086165463    18102757.72    301712.6    12571.35953    34.44208089       
444    1095608694    18260144.9    304335.7    12680.65618    34.74152378       
445    1105105765    18418429.42    306973.8    12790.57598    35.04267393       
446    1114672773    18577879.55    309631.3    12901.30524    35.34604176       
447    1124291181    18738186.35    312303.1    13012.62941    35.65103948       
448    1133980103    18899668.38    314994.5    13124.76971    35.95827318       
449    1143722314    19062038.57    317700.6    13237.52678    36.26719666       
450    1153534157    19225569.28    320426.2    13351.08978    36.57832816       
451    1163401204    19390020.07    323167    13465.29171    36.89121017       
452    1173338464    19555641.07    325927.4    13580.3063    37.20631862       
453    1183329899    19722164.98    328702.7    13695.94791    37.52314495       
454    1193392119    19889868.65    331497.8    13812.40878    37.84221585       
455    1203510455    20058507.58    334308.5    13929.51916    38.16306618       
456    1213700162    20228336.03    337138.9    14047.45558    38.48617967       
457    1223944936    20399082.27    339984.7    14166.02935    38.81103932       
458    1234261657    20571027.62    342850.5    14285.43584    39.1381804       
459    1244635414    20743923.57    345732.1    14405.50248    39.46713007       
460    1255081708    20918028.47    348633.8    14526.40866    39.79837988       
461    1265583968    21093066.13    351551.1    14647.96259    40.13140436       
462    1276159345    21269322.42    354488.7    14770.36279    40.46674737       
463    1286792686    21446544.77    357442.4    14893.43387    40.8039284       
464    1297499738    21624995.63    360416.6    15017.35808    41.14344679       
465    1308263663    21804394.38    363406.6    15141.94054    41.48476861       
466    1319103453    21985057.55    366417.6    15267.40108    41.8284961       
467    1329999003    22166650.05    369444.2    15393.50698    42.17399172       
468    1340971016    22349516.93    372491.9    15520.49787    42.52191197       
469    1352000815    22533346.92    375555.8    15648.15758    42.87166461       
470    1363107691    22718461.52    378641    15776.70939    43.22386133       
471    1374272820    22904547    381742.5    15905.93542    43.57790525       
472    1385512427    23091873.78    384864.6    16036.02346    43.93431085       
473    1396813955    23280232.58    388003.9    16166.82818    44.29267995       
474    1408190554    23469842.57    391164    16298.50178    44.65342954       
475    1419627942    23660465.7    394341.1    16430.87896    45.01610674       
476    1431142617    23852376.95    397539.6    16564.15066    45.38123468       
477    1442716925    24045282.08    400754.7    16698.11256    45.74825358       
478    1454370762    24239512.7    403991.9    16832.99493    46.11779433       
479    1466083053    24434717.55    407245.3    16968.55385    46.48918864       
480    1477875486    24631258.1    410521    17105.04035    46.86312424       
481    1489730148    24828835.8    413813.9    17242.24708    47.23903311       
482    1501662251    25027704.18    417128.4    17380.35013    47.61739761       
483    1513657061    25227617.68    420460.3    17519.17895    47.99775054       
484    1525731584    25428859.73    423814.3    17658.93037    48.38063115       
485    1537867615    25631126.92    427185.4    17799.39369    48.76546217       
486    1550085662    25834761.03    430579.4    17940.80627    49.1528939       
487    1562365695    26039428.25    433990.5    18082.93628    49.54229119       
488    1574726670    26245444.5    437424.1    18226.00313    49.93425514       
489    1587150098    26452501.63    440875    18369.7928    50.32819945       
490    1599655079    26660917.98    444348.6    18514.52638    50.7247298       
491    1612224711    26870411.85    447840.2    18660.00823    51.12331022       
492    1624876521    27081275.35    451354.6    18806.44122    51.52449648       
493    1637593478    27293224.63    454887.1    18953.62822    51.92774854       
494    1650391494    27506524.9    458442.1    19101.7534    52.33357097       
495    1663255144    27720919.07    462015.3    19250.63824    52.74147463       
496    1676202217    27936703.62    465611.7    19400.48862    53.15202362       
497    1689215424    28153590.4    469226.5    19551.10444    53.56466971       
498    1702310912    28371848.53    472864.1    19702.67259    53.97992491       
499    1715473024    28591217.07    476520.3    19855.01185    54.39729274       
500    1728719812    28811996.87    480199.9    20008.33116    54.81734564       
501    1742033728    29033895.47    483898.3    20162.42741    55.23952714       
502    1755431156    29257185.93    487619.8    20317.49023    55.6643568       
503    1768896206    29481603.43    491360.1    20473.33572    56.09133073       
504    1782447193    29707453.22    495124.2    20630.17584    56.52102971       
505    1796066309    29934438.48    498907.3    20787.8045    56.95288905       
506    1809770176    30162836.27    502713.9    20946.41407    57.38743582       
507    1823542669    30392377.82    506539.6    21105.81793    57.82415871       
508    1837402370    30623372.83    510389.5    21266.23113    58.26364694       
509    1851331207    30855520.12    514258.7    21427.44453    58.70532747       
510    1865346045    31089100.75    518151.7    21589.6533    59.14973506       
511    1879430518    31323841.97    522064    21752.66803    59.59635077       
512    1893603479    31560057.98    526001    21916.70693    60.04577242       
513    1907846590    31797443.17    529957.4    22081.55775    60.49741851       
514    1922178838    32036313.97    533938.6    22247.44025    60.95189111       
515    1936579867    32276331.12    537938.9    22414.11883    61.40854474       
516    1951070671    32517844.52    541964.1    22581.83647    61.86804512       
517    1965630747    32760512.45    546008.5    22750.35587    62.3297421       
518    1980283146    33004719.1    550078.7    22919.94382    62.79436663       
519    1995005322    33250088.7    554168.1    23090.33938    63.26120377       
520    2009818571    33496976.18    558282.9    23261.78902    63.73092881       
521    2024704019    33745066.98    562417.8    23434.07429    64.20294327       
522    2039679265    33994654.42    566577.6    23607.3989    64.67780521       
523    2054727219    34245453.65    570757.6    23781.56503    65.1549727       
524    2069869499    34497824.98    574963.7    23956.82291    65.63513125       
525    2085081118    34751351.97    579189.2    24132.88331    66.11748852       
526    2100387725    35006462.08    583441    24310.04311    66.60285785       
527    2115766125    35262768.75    587712.8    24488.03385    67.09050371       
528    2131238217    35520636.95    592010.6    24667.10899    67.58112053       
529    2146784586    35779743.1    596329.1    24847.04382    68.07409266       
530    2162425313    36040421.88    600673.7    25028.07075    68.57005686       
531    2178138851    36302314.18    605038.6    25209.94041    69.06832988       
532    2193947404    36565790.07    609429.8    25392.90977    69.5696158       
533    2209829272    36830487.87    613841.5    25576.72769    70.07322653       
534    2225808829    37096813.82    618280.2    25761.67626    70.57993496       
535    2241862221    37364370.35    622739.5    25947.47941    71.08898468       
536    2258013989    37633566.48    627226.1    26134.42117    71.60115389       
537    2274238077    37903967.95    631732.8    26322.19997    72.11561634       
538    2290561218    38176020.3    636267    26511.12521    72.63321975       
539    2306959224    38449320.4    640822    26700.91694    73.15319711       
540    2323454917    38724248.62    645404.1    26891.83932    73.6762721       
541    2340028052    39000467.53    650007.8    27083.65801    74.20180277       
542    2356699554    39278325.9    654638.8    27276.61521    74.73045263       
543    2373446960    39557449.33    659290.8    27470.45093    75.26150939       
544    2390293400    39838223.33    663970.4    27665.43287    75.79570649       
545    2407218352    40120305.87    668671.8    27861.32352    76.3323932       
546    2424243024    40404050.4    673400.8    28058.36833    76.87224201       
547    2441344644    40689077.4    678151.3    28256.30375    77.41453082       
548    2458546656    40975777.6    682929.6    28455.40111    77.96000304       
549    2475828257    41263804.28    687730.1    28655.41964    78.50799902       
550    2493210938    41553515.63    692558.6    28856.60808    79.05920022       
551    2510671619    41844526.98    697408.8    29058.69929    79.61287478       
552    2528236201    42137270.02    702287.8    29261.99307    80.16984402       
553    2545877167    42431286.12    707188.1    29466.17091    80.72923538       
554    2563622728    42727045.47    712117.4    29671.55935    81.29194343       
555    2581447347    43024122.45    717068.7    29877.86281    81.85715839       
556    2599377270    43322954.5    722049.2    30085.38507    82.42571252       
557    2617386789    43623113.15    727051.9    30293.82858    82.99679062       
558    2635497951    43924965.85    732082.8    30503.44851    83.5710918       
559    2653693608    44228226.8    737137.1    30714.04639    84.1480723       
560    2671991595    44533193.25    742219.9    30925.82865    84.72829766       
561    2690372439    44839540.65    747325.7    31138.5699    85.3111504       
562    2708858500    45147641.67    752460.7    31352.52894    85.89733955       
563    2727425755    45457095.92    757618.3    31567.42772    86.48610334       
564    2746098916    45768315.27    762805.3    31783.55227    87.07822539       
565    2764856039    46080933.98    768015.6    32000.6486    87.67300986       
566    2783719775    46395329.58    773255.5    32218.97888    88.27117501       
567    2802668034    46711133.9    778518.9    32438.28743    88.87202036       
568    2821721356    47028689.27    783811.5    32658.81199    89.47619723       
569    2840859749    47347662.48    789127.7    32880.32117    90.0830717       
570    2860106161    47668436.02    794473.9    33103.08057    90.69337142       
571    2879435928    47990598.8    799843.3    33326.80472    91.30631431       
572    2898876699    48314611.65    805243.5    33551.81365    91.92277711       
573    2918399082    48639984.7    810666.4    33777.76715    92.54182782       
574    2938033185    48967219.75    816120.3    34005.01372    93.16442114       
575    2957754045    49295900.75    821598.3    34233.26441    93.78976551       
576    2977582735    49626378.92    827106.3    34462.76314    94.41852914       
577    2997498738    49958312.3    832638.5    34693.27243    95.05006145       
578    3017525594    50292093.23    838201.6    34925.06475    95.68510889       
579    3037637995    50627299.92    843788.3    35157.84716    96.32286894       
580    3057864302    50964405.03    849406.8    35391.94794    96.96424093       
581    3078176713    51302945.22    855049.1    35627.04529    97.60834326       
582    3098601407    51643356.78    860722.6    35863.44221    98.25600606       
583    3119112750    51985212.5    866420.2    36100.84201    98.90641648       
584    3139739464    52328991.07    872149.9    36339.57713    99.56048529       
585    3160453390    52674223.17    877903.7    36579.32164    100.2173196       
586    3181281037    53021350.62    883689.2    36820.38237    100.8777599       
587    3202196444    53369940.73    889499    37062.45884    101.5409831       
588    3223228697    53720478.28    895341.3    37305.8877    102.2079115       
589    3244349274    54072487.9    901208.1    37550.33882    102.8776406       
590    3265585021    54426417.02    907107    37796.12293    103.5510217       
591    3286909645    54781827.42    913030.5    38042.93571    104.2272211       
592    3308352597    55139209.95    918986.8    38291.11802    104.9071727       
593    3329884994    55498083.23    924968.1    38540.33558    105.5899605       
594    3351534018    55858900.3    930981.7    38790.90299    106.2764465       
595    3373273042    56221217.37    937020.3    39042.51206    106.9657865       
596    3395131885    56585531.42    943092.2    39295.50793    107.6589258       
597    3417081300    56951355    949189.3    39549.55208    108.3549372       
598    3439148807    57319146.78    955319.1    39804.96304    109.0546933       
599    3461309936    57688498.93    961475    40061.45759    109.7574181       
600    3483587401    58059790.02    967663.2    40319.29862    110.4638318       
601    3505959064    58432651.07    973877.5    40578.22991    111.1732326       
602    3528450291    58807504.85    980125.1    40838.54503    111.8864248       
603    3551036309    59183938.48    986399    41099.95728    112.6026227       
604    3573742638    59562377.3    992706.3    41362.76201    113.3226357       
605    3596541816    59942363.6    999039.4    41626.64139    114.0455928       
606    3619462039    60324367.32    1005406    41891.92175    114.7723883       
607    3642475675    60707927.92    1011799    42158.28328    115.502146       
608    3665613654    61093560.9    1018226    42426.08396    116.2358465       
609    3688845628    61480760.47    1024679    42694.97255    116.9725275       
610    3712200138    61870002.3    1031167    42965.27938    117.7130942       
611    3735651796    62260863.27    1037681    43236.7106    118.4567414       
612    3759224153    62653735.88    1044229    43509.53881    119.2042159       
613    3782894244    63048237.4    1050804    43783.49819    119.9547896       
614    3806690977    63444849.62    1057414    44058.92334    120.709379       
615    3830580831    63843013.85    1064050    44335.42628    121.4669213       
616    3854598088    64243301.47    1070722    44613.4038    122.2285036       
617    3878711654    64645194.23    1077420    44892.496    122.9931397       
618    3902950762    65049179.37    1084153    45173.04123    123.7617568       
619    3927289401    65454823.35    1090914    45454.73844    124.53353       
620    3951754347    65862572.45    1097710    45737.89753    125.3093083       
621    3976316769    66271946.15    1104532    46022.18483    126.0881776       
622    4001006249    66683437.48    1111391    46307.9427    126.8710759       
623    4025796462    67096607.7    1118277    46594.86646    127.6571684       
624    4050711815    67511863.58    1125198    46883.2386    128.447229       
625    4075731191    67928853.18    1132148    47172.81471    129.2405882       
626    4100876463    68347941.05    1139132    47463.84795    130.0379396       
627    4126123677    68768727.95    1146145    47756.06108    130.8385235       
628    4151497527    69191625.45    1153194    48049.7399    131.643123       
629    4176973918    69616231.97    1160271    48344.60553    132.4509741       
630    4202583158    70043052.63    1167384    48641.00877    133.2630377       
631    4228290087    70471501.45    1174525    48938.54267    134.0781991       
632    4254130642    70902177.37    1181703    49237.62317    134.8975977       
633    4280072214    71334536.9    1188909    49537.87285    135.7201996       
634    4306148209    71769136.82    1196152    49839.67834    136.547064       
635    4332323050    72205384.17    1203423    50142.62789    137.3770627       
636    4358633095    72643884.92    1210731    50447.1423    138.2113488       
637    4385048142    73084135.7    1218069    50752.87201    139.0489644       
638    4411593611    73526560.18    1225443    51060.11124    139.8907157       
639    4438244689    73970744.82    1232846    51368.57279    140.7358159       
640    4465026943    74417115.72    1240285    51678.55258    141.5850756       
641    4491918238    74865303.97    1247755    51989.79442    142.4377929       
642    4518941482    75315691.37    1255262    52302.56345    143.2946944       
643    4546071569    75767859.48    1262798    52616.56909    144.1549838       
644    4573337211    76222286.85    1270371    52932.14365    145.0195716       
645    4600707469    76678457.82    1277974    53248.92904    145.8874768       
646    4628214058    77136900.97    1285615    53567.29234    146.759705       
647    4655828733    77597145.55    1293286    53886.90663    147.6353606       
648    4683580533    78059675.55    1300995    54208.10802    148.5153644       
649    4711438163    78523969.38    1308733    54530.53429    149.3987241       
650    4739436595    78990609.92    1316510    54854.59022    150.2865485       
651    4767538569    79458976.15    1324316    55179.84455    151.1776563       
652    4795782145    79929702.42    1332162    55506.73779    152.0732542       
653    4824135691    80402261.52    1340038    55834.90383    152.9723393       
654    4852625813    80877096.88    1347952    56164.65061    153.8757551       
655    4881226526    81353775.43    1355896    56495.67738    154.7826778       
656    4909967532    81832792.2    1363880    56828.32792    155.6940491       
657    4938816813    82313613.55    1371894    57162.23163    156.6088538       
658    4967810137    82796835.62    1379947    57497.80251    157.5282261       
659    4996912362    83281872.7    1388031    57834.63382    158.4510516       
660    5026156474    83769274.57    1396155    58173.10734    159.3783763       
661    5055510095    84258501.58    1404308    58512.84832    160.3091735       
662    5085006397    84750106.62    1412502    58854.24071    161.2444951       
663    5114615822    85243597.03    1420727    59196.94238    162.1834038       
664    5144368741    85739479.02    1428991    59541.30487    163.1268627       
665    5174235428    86237257.13    1437288    59886.98412    164.0739291       
666    5204243392    86737389.87    1445623    60234.29852    165.0254754       
667    5234365756    87239429.27    1453990    60582.93699    165.9806493       
668    5264633226    87743887.1    1462398    60933.25493    166.9404245       
669    5295012688    88250211.47    1470837    61284.86907    167.9037509       
670    5325541122    88759018.7    1479317    61638.20743    168.8718012       
671    5356182183    89269703.05    1487828    61992.84934    169.8434229       
672    5386969971    89782832.85    1496381    62349.18948    170.8196972       
673    5417871005    90297850.08    1504964    62706.84034    171.7995626       
674    5448922669    90815377.82    1513590    63066.23459    172.7842044       
675    5480088216    91334803.6    1522247    63426.94694    173.7724574       
676    5511402121    91856702.02    1530945    63789.3764    174.7654148       
677    5542830529    92380508.82    1539675    64153.13112    175.7620031       
678    5574411236    92906853.93    1548448    64518.64856    176.7634207       
679    5606107088    93435118.13    1557252    64885.4987    177.7684896       
680    5637952936    93965882.27    1566098    65254.08491    178.7783148       
681    5669914553    94498575.88    1574976    65624.01103    179.791811       
682    5702030146    95033835.77    1583897    65995.71928    180.8101898       
683    5734262152    95571035.87    1592851    66368.77491    181.83226       
684    5766645801    96110763.35    1601846    66743.58566    182.8591388       
685    5799146491    96652441.52    1610874    67119.75105    183.8897289       
686    5831802842    97196714.03    1619945    67497.71808    184.925255       
687    5864576880    97742948    1629049    67877.04722    185.9645129       
688    5897504218    98291736.97    1638196    68258.15067    187.008632       
689    5930553100    98842551.67    1647376    68640.66088    188.0566051       
690    5963752886    99395881.43    1656598    69024.91766    189.1093635       
691    5997074867    99951247.78    1665854    69410.58874    190.1659965       
692    6030555062    100509251    1675154    69798.091    191.2276466       
693    6064151617    101069193.6    1684487    70186.94001    192.2929863       
694    6097907231    101631787.2    1693863    70577.62999    193.3633698       
695    6131783102    102196385    1703273    70969.71183    194.4375667       
696    6165815607    102763593.5    1712727    71363.60656    195.5167303       
697    6199972302    103332871.7    1722215    71758.93868    196.599832       
698    6234283176    103904719.6    1731745    72156.05528    197.6878227       
699    6268718897    104478648.3    1741311    72554.61686    198.7797722       
700    6303316254    105055270.9    1750921    72955.04924    199.8768472       
701    6338032492    105633874.9    1760565    73356.85755    200.9776919       
702    6372911217    106215187    1770253    73760.54649    202.083689       
703    6407912796    106798546.6    1779976    74165.65736    203.1935818       
704    6443074379    107384573    1789743    74572.62013    204.3085483       
705    6478362824    107972713.7    1799545    74981.0512    205.4275375       
706    6513808755    108563479.3    1809391    75391.30503    206.5515206       
707    6549385595    109156426.6    1819274    75803.07402    207.6796548       
708    6585120761    109752012.7    1829200    76216.67547    208.8128095       
709    6620980736    110349678.9    1839161    76631.72148    209.9499219       
710    6657006664    110950111.1    1849169    77048.68824    211.0922965       
711    6693158066    111552634.4    1859211    77467.10725    212.23865       
712    6729476303    112157938.4    1869299    77887.45721    213.3902937       
713    6765917246    112765287.4    1879421    78309.22738    214.5458285       
714    6802525887    113375431.5    1889591    78732.93851    215.7066808       
715    6839261324    113987688.7    1899795    79158.11718    216.8715539       
716    6876161881    114602698    1910045    79585.20696    218.0416629       
717    6913193359    115219889.3    1920331    80013.81203    219.2159234       
718    6950390827    115839847.1    1930664    80444.33828    220.3954473       
719    6987716417    116461940.3    1941032    80876.34742    221.579034       
720    7025208849    117086814.2    1951447    81310.2876    222.7679112       
721    7062833568    117713892.8    1961898    81745.75889    223.9609833       
722    7100626004    118343766.7    1972396    82183.17134    225.1593735       
723    7138547895    118975798.3    1982930    82622.08212    226.3618688       
724    7176638359    119610639.3    1993511    83062.94397    227.5697095       
725    7214862483    120247708.1    2004128    83505.35281    228.7817885       
726    7253256058    120887601    2014793    83949.72289    229.9992408       
727    7291780429    121529673.8    2025495    84395.60682    231.2208406       
728    7330478683    122174644.7    2036244    84843.50328    232.4479542       
729    7369304834    122821747.2    2047029    85292.88002    233.6791234       
730    7408305750    123471762.5    2057863    85744.27951    234.9158343       
731    7447438808    124123980.1    2068733    86197.20843    236.1567354       
732    7486747533    124779125.6    2079652    86652.17052    237.4032069       
733    7526189086    125436484.8    2090608    87108.66998    238.6538903       
734    7565803584    126096726.4    2101612    87567.17111    239.9100578       
735    7605551576    126759192.9    2112653    88027.21731    241.1704584       
736    7645473384    127424556.4    2123743    88489.27528    242.4363706       
737    7685533010    128092216.8    2134870    88952.92836    243.706653       
738    7725767342    128762789    2146046    89418.6035    244.9824753       
739    7766136528    129435608.8    2157260    89885.83944    246.2625738       
740    7806684974    130111416.2    2168524    90355.15016    247.5483566       
741    7847365276    130789421.3    2179824    90825.98699    248.8383205       
742    7888225732    131470428.9    2191174    91298.90894    250.1339971       
743    7929226117    132153768.6    2202563    91773.45043    251.4341108       
744    7970400154    132840002.6    2214000    92250.00178    252.7397309       
745    8011714815    133528580.3    2225476    92728.18073    254.0498102       
746    8053207726    134220128.8    2237002    93208.42275    255.3655418       
747    8094838229    134913970.5    2248566    93690.25728    256.6856364       
748    8136651619    135610860.3    2260181    94174.20855    258.0115303       
749    8178603300    136310055    2271834    94659.76042    259.3418094       
750    8220735016    137012250.3    2283538    95147.39602    260.6777973       
751    8263005703    137716761.7    2295279    95636.64008    262.018192       
752    8305457311    138424288.5    2307071    96127.97814    263.3643237       
753    8348052374    139134206.2    2318903    96620.97655    264.7150042       
754    8390829266    139847154.4    2330786    97116.07947    266.0714506       
755    8433750334    140562505.6    2342708    97612.85109    267.4324687       
756    8476850311    141280838.5    2354681    98111.69341    268.79916       
757    8520095167    142001586.1    2366693    98612.21258    270.1704454       
758    8563523654    142725394.2    2378757    99114.85711    271.5475537       
759    8607097746    143451629.1    2390860    99619.18688    272.9292791       
760    8650852515    144180875.3    2403015    100125.6078    274.3167337       
761    8694753597    144912560    2415209    100633.7222    275.7088279       
762    8738840118    145647335.3    2427456    101143.9828    277.1068023       
763    8783073681    146384561.4    2439743    101655.9454    278.5094394       
764    8827489696    147124828.3    2452080    102170.0196    279.917862       
765    8872053463    147867557.7    2464459    102685.804    281.3309698       
766    8916804489    148613408.2    2476890    103203.7557    282.7500155       
767    8961703997    149361733.3    2489362    103723.4259    284.1737696       
768    9006787743    150113129.1    2501885    104245.2285    285.6033658       
769    9052020686    150867011.4    2514450    104768.7579    287.037693       
770    9097442714    151624045.2    2527067    105294.4759    288.478016       
771    9143014674    152383577.9    2539726    105821.9291    289.9230934       
772    9188772665    153146211.1    2552437    106351.5355    291.3740698       
773    9234681304    153911355.1    2565189    106882.8855    292.8298232       
774    9280780863    154679681.1    2577995    107416.4452    294.2916306       
775    9327031810    155450530.2    2590842    107951.7571    295.7582385       
776    9373474606    156224576.8    2603743    108489.2894    297.2309299       
777    9420065501    157001091.7    2616685    109028.5359    298.7083175       
778    9466849159    157780819.3    2629680    109570.0134    300.1918176       
779    9513781619    158563027    2642717    110113.2132    301.6800361       
780    9560911814    159348530.2    2655809    110658.7016    303.1745248       
781    9608191534    160136525.6    2668942    111205.9205    304.6737549       
782    9655665869    160927764.5    2682129    111755.392    306.1791562       
783    9703294522    161721575.4    2695360    112306.6496    307.6894508       
784    9751114632    162518577.2    2708643    112860.1231    309.2058166       
785    9799089787    163318163.1    2721969    113415.3911    310.7270988       
786    9847265531    164121092.2    2735352    113972.9807    312.2547416       
787    9895588838    164926480.6    2748775    114532.2782    313.7870636       
788    9944113676    165735227.9    2762254    115093.9083    315.3257761       
789    9992790914    166546515.2    2775775    115657.3022    316.8693212       
790    10041666493    167361108.2    2789352    116222.9918    318.4191557       
791    10090699348    168178322.5    2802972    116790.5017    319.9739773       
792    10139927318    168998788.6    2816646    117360.2699    321.534986       
793    10189317479    169821958    2830366    117931.9153    323.1011377       
794    10238903686    170648394.8    2844140    118505.8297    324.673506       
795    10288644453    171477407.6    2857957    119081.533    326.2507754       
796    10338590582    172309843    2871831    119659.6132    327.8345568       
797    10388692009    173144866.8    2885748    120239.4908    329.4232626       
798    10438999770    173983329.5    2899722    120821.7566    331.0185112       
799    10489459326    174824322.1    2913739    121405.7792    332.6185732       
800    10540126172    175668769.5    2927813    121992.2011    334.2252084       
801    10590949774    176515829.6    2941930    122580.4372    335.8368142       
802    10641977372    177366289.5    2956105    123171.0344    337.4548888       
803    10693166729    178219445.5    2970324    123763.5038    339.0780926       
804    10744561042    179076017.4    2984600    124358.3454    340.7077956       
805    10796113576    179935226.3    2998920    124955.0182    342.3425157       
806    10847872007    180797866.8    3013298    125554.0742    343.9837648       
807    10899793706    181663228.4    3027720    126155.0197    345.6301911       
808    10951922265    182532037.8    3042201    126758.3595    347.2831768       
809    11004210517    183403508.6    3056725    127363.5477    348.9412264       
810    11056706576    184278442.9    3071307    127971.1409    350.6058656       
811    11109367417    185156123.6    3085935    128580.6414    352.2757299       
812    11162237031    186037283.9    3100621    129192.5582    353.9522143       
813    11215267818    186921130.3    3115352    129806.3405    355.6338096       
814    11268508328    187808472.1    3130141    130422.5501    357.322055       
815    11321915141    188698585.7    3144976    131040.6845    359.015574       
816    11375532650    189592210.8    3159870    131661.2575    360.715774       
817    11429312815    190488546.9    3174809    132283.7131    362.4211319       
818    11483309060    191388484.3    3189808    132908.6697    364.1333416       
819    11537464276    192291071.3    3204851    133535.4662    365.8505922       
820    11591836547    193197275.8    3219955    134164.7748    367.5747256       
821    11646377426    194106290.4    3235105    134796.035    369.3042055       
822    11701127438    195018790.6    3250313    135429.7157    371.040317       
823    11756046816    195934113.6    3265569    136065.3567    372.7817991       
824    11811180758    196853012.6    3280884    136703.481    374.5300849       
825    11866480343    197774672.4    3296245    137343.5225    376.2836233       
826    11921995455    198699924.3    3311665    137986.0585    378.0439959       
827    11977681473    199628024.6    3327134    138630.5726    379.809788       
828    12033584001    200559733.4    3342662    139277.5926    381.5824455       
829    12089653678    201494228    3358237    139926.5472    383.3604033       
830    12145945382    202432423    3373874    140578.0716    385.1454015       
831    12202404999    203373416.7    3389557    141231.5393    386.9357242       
832    12259083080    204318051.3    3405301    141887.5356    388.7329744       
833    12315929820    205265497    3421092    142545.484    390.5355727       
834    12372995995    206216599.9    3436943    143205.9722    392.3451292       
835    12430236178    207170603    3452843    143868.4743    394.1602035       
836    12487696788    208128279.8    3468805    144533.5276    395.9822675       
837    12545332196    209088869.9    3484814    145200.6041    397.8098743       
838    12603184393    210053073.2    3500885    145870.1897    399.6443554       
839    12661212159    211020202.7    3517003    146541.8074    401.4844038       
840    12719462324    211991038.7    3533184    147215.9991    403.3315044       
841    12777884186    212964736.4    3549412    147892.1781    405.1840495       
842    12836534099    213942235    3565704    148570.9965    407.0438261       
843    12895356484    214922608.1    3582043    149251.8112    408.9090717       
844    12954403247    215906720.8    3598445    149935.2228    410.7814322       
845    13013623237    216893720.6    3614895    150620.6393    412.6592858       
846    13073073303    217884555.1    3631409    151308.7188    414.544435       
847    13132697372    218878289.5    3647971    151998.8122    416.4351019       
848    13192547808    219875796.8    3664597    152691.5256    418.3329467       
849    13252573006    220876216.8    3681270    153386.2616    420.2363333       
850    13312830312    221880505.2    3698008    154083.6842    422.1470799       
851    13373263162    222887719.4    3714795    154783.1384    424.063393       
852    13433924373    223898739.6    3731646    155485.2358    425.9869474       
853    13494761888    224912698.1    3748545    156189.3737    427.9160923       
854    13555833553    225930559.2    3765509    156896.2217    429.8526621       
855    13617082306    226951371.8    3782523    157605.1193    431.7948473       
856    13678561425    227976023.8    3799600    158316.6832    433.7443374       
857    13740218396    229003639.9    3816727    159030.3055    435.6994671       
858    13802111568    230035192.8    3833920    159746.6617    437.6620868       
859    13864183378    231069723    3851162    160465.0854    439.6303709       
860    13926487566    232108126.1    3868469    161186.1987    441.6060238       
861    13988971161    233149519.4    3885825    161909.3884    443.5873656       
862    14051693015    234194883.6    3903248    162635.3358    445.5762625       
863    14114595065    235243251.1    3920721    163363.3688    447.5708734       
864    14177731514    236295525.2    3938259    164094.1147    449.5729171       
865    14241053844    237350897.4    3955848    164827.0121    451.580855       
866    14304606672    238410111.2    3973502    165562.5772    453.596102       
867    14368346174    239472436.2    3991207    166300.3029    455.6172683       
868    14432327049    240538784.2    4008980    167040.8223    457.6460886       
869    14496485524    241608092.1    4026802    167783.3973    459.6805405       
870    14560886399    242681440    4044691    168528.7778    461.7226788       
871    14625470605    243757843.4    4062631    169276.2802    463.7706305       
872    14690293275    244838221.3    4080637    170026.5425    465.8261439       
873    14755305051    245921750.9    4098696    170778.9936    467.8876538       
874    14820551315    247009188.6    4116820    171534.1587    469.9565993       
875    14885987485    248099791.4    4134997    172291.5218    472.0315666       
876    14951669194    249194486.6    4153241    173051.7268    474.11432       
877    15017531571    250292192.9    4171537    173814.0228    476.2028022       
878    15083640524    251394008.7    4189900    174579.1727    478.2991034       
879    15149935968    252498932.8    4208316    175346.4811    480.4013181       
880    15216473974    253607899.6    4226798    176116.5969    482.5112244       
881    15283204338    254720072.3    4245335    176888.9391    484.6272304       
882    15350173210    255836220.2    4263937    177664.0418    486.7507994       
883    15417340351    256955672.5    4282595    178441.4392    488.8806555       
884    15484747022    258079117    4301319    179221.6091    491.018107       
885    15552342559    259205709.3    4320095    180003.9648    493.1615474       
886    15620188880    260336481.3    4338941    180789.2231    495.3129401       
887    15688224878    261470414.6    4357840    181576.6768    497.4703475       
888    15756512726    262608545.4    4376809    182367.0454    499.6357409       
889    15824985893    263749764.9    4395829    183159.5589    501.8070108       
890    15893711961    264895199.4    4414920    183954.9995    503.9863001       
891    15962629306    266043821.8    4434064    184752.654    506.1716548       
892    16031800624    267196677.1    4453278    185553.248    508.3650629       
893    16101158823    268352647.1    4472544    186356.0049    510.564397       
894    16170772047    269512867.5    4491881    187161.7135    512.7718178       
895    16240578157    270676302.6    4511272    187969.6546    514.9853551       
896    16310640369    271844006.2    4530733    188780.5598    517.2070132       
897    16380891030    273014850.5    4550248    189593.6462    519.4346471       
898    16451398850    274189980.8    4569833    190409.7089    521.6704354       
899    16522101171    275368352.9    4589473    191228.0228    523.9123913       
900    16593061731    276551028.9    4609184    192049.3256    526.1625359       
901    16664212314    277736871.9    4628948    192872.8277    528.4187061       
902    16735622198    278927036.6    4648784    193699.331    530.6830986       
903    16807228204    280120470.1    4668675    194528.1042    532.9537102       
904    16879094595    281318243.3    4688637    195359.8911    535.2325785       
905    16951157933    282519298.9    4708655    196193.9576    537.5176919       
906    17023472036    283724533.9    4728742    197030.9263    539.8107571       
907    17095994596    284933243.3    4748887    197870.3078    542.1104324       
908    17168768965    286146149.4    4769102    198712.6038    544.4180925       
909    17241747277    287362454.6    4789374    199557.2602    546.7322196       
910    17314983821    288583063.7    4809718    200404.9053    549.0545352       
911    17388419750    289806995.8    4830117    201254.8582    551.3831732       
912    17462114960    291035249.3    4850587    202107.812    553.720033       
913    17536015793    292266929.9    4871115    202963.1458    556.063413       
914    17610176982    293502949.7    4891716    203821.4928    558.4150489       
915    17684539194    294742319.9    4912372    204682.1666    560.7730592       
916    17759168279    295986138    4933102    205545.9292    563.1395319       
917    17833999221    297233320.4    4953889    206412.028    565.5124055       
918    17909092649    298484877.5    4974748    207281.1649    567.8936025       
919    17984388748    299739812.5    4995664    208152.6475    570.2812262       
920    18059948390    300999139.8    5016652    209027.1804    572.6772067       
921    18135717037    302261950.6    5037699    209904.1324    575.0798147       
922    18211750308    303529171.8    5058820    210784.1471    577.4908139       
923    18287993443    304799890.7    5079998    211666.5908    579.9084679       
924    18364496735    306074945.6    5101249    212552.0455    582.3343714       
925    18441210731    307353512.2    5122559    213439.939    584.7669562       
926    18518191498    308636525    5143942    214330.9201    587.2080003       
927    18595378248    309922970.8    5165383    215224.2853    589.6555761       
928    18672838433    311213973.9    5186900    216120.8152    592.1118225       
929    18750505442    312508424    5208474    217019.7389    594.5746272       
930    18828441379    313807356.3    5230123    217921.7752    597.0459595       
931    18906584963    315109749.4    5251829    218826.2148    599.5238763       
932    18985004185    316416736.4    5273612    219733.8447    602.0105335       
933    19063631902    317727198.4    5295453    220643.8878    604.5038021       
934    19142530708    319042178.5    5317370    221557.0684    607.0056668       
935    19221638834    320360647.2    5339344    222472.6717    609.514169       
936    19301024810    321683746.8    5361396    223391.4909    612.0314818       
937    19380615256    323010254.3    5383504    224312.6766    614.5552783       
938    19460490361    324341506    5405692    225237.157    617.0881012       
939    19540570764    325676179.4    5427936    226164.0135    619.6274342       
940    19620931239    327015520.7    5450259    227094.1116    622.1756481       
941    19701497819    328358297    5472638    228026.5951    624.7303976       
942    19782351328    329705855.5    5495098    228962.3996    627.2942456       
943    19863411775    331056862.9    5517614    229900.5992    629.8646555       
944    19944754521    332412575.4    5540210    230842.0662    632.444017       
945    20026310805    333771846.8    5562864    231786.0047    635.0301498       
946    20108144717    335135745.3    5585596    232733.1564    637.6250862       
947    20190193001    336503216.7    5608387    233682.7894    640.2268202       
948    20272525822    337875430.4    5631257    234635.7155    642.8375768       
949    20355073874    339251231.2    5654187    235591.1328    645.4551584       
950    20437901750    340631695.8    5677195    236549.7888    648.0816131       
951    20520945695    342015761.6    5700263    237510.9455    650.7149193       
952    20604276422    343404607    5723410    238475.4216    653.3573193       
953    20687824079    344797068    5746618    239442.4083    656.0065981       
954    20771653766    346194229.4    5769904    240412.6593    658.6648201       
955    20855707126    347595118.8    5793252    241385.4991    661.3301346       
956    20940037717    349000628.6    5816677    242361.5477    664.0042401       
957    21024592848    350409880.8    5840165    243340.195    666.6854658       
958    21109438156    351823969.3    5863733    244322.2009    669.3758928       
959    21194497019    353241617    5887360    245306.6785    672.0730917       
960    21279847181    354664119.7    5911069    246294.5276    674.7795276       
961    21365417692    356090294.9    5934838    247284.927    677.4929507       
962    21451274663    357521244.4    5958687    248278.6419    680.2154574       
963    21537358825    358955980.4    5982600    249274.9864    682.9451682       
964    21623724566    360395409.4    6006590    250274.5899    685.6838079       
965    21710324388    361838739.8    6030646    251276.9026    688.4298702       
966    21797206893    363286781.6    6054780    252282.4872    691.1848964       
967    21884312315    364738538.6    6078976    253290.6518    693.9469912       
968    21971713584    366195226.4    6103254    254302.2406    696.7184673       
969    22059338647    367655644.1    6127594    255316.4195    699.4970398       
970    22147254634    369120910.6    6152015    256333.9657    702.2848375       
971    22235401355    370590022.6    6176500    257354.1823    705.0799516       
972    22323840134    372064002.2    6201067    258377.7793    707.8843269       
973    22412504438    373541740.6    6225696    259403.9866    710.6958536       
974    22501461910    375024365.2    6250406    260433.5869    713.5166765       
975    22590651898    376510865    6275181    261465.8784    716.3448725       
976    22680136192    378002269.9    6300038    262501.5763    719.1824008       
977    22769847747    379497462.5    6324958    263539.9045    722.0271356       
978    22859854725    380997578.8    6349960    264581.6519    724.8812381       
979    22950096004    382501600.1    6375027    265626.1112    727.7427703       
980    23040633847    384010564.1    6400176    266674.0029    730.6137065       
981    23131400695    385523344.9    6425389    267724.5451    733.4919043       
982    23222465226    387041087.1    6450685    268778.5327    736.3795417       
983    23313765853    388562764.2    6476046    269835.2529    739.2746656       
984    23405365307    390089421.8    6501490    270895.4318    742.1792652       
985    23497195517    391619925.3    6526999    271958.2814    745.091182       
986    23589325678    393155428    6552590    273024.6028    748.0126103       
987    23681693735    394694895.6    6578248    274093.6775    750.9415822       
988    23774362893    396239381.6    6603990    275166.2372    753.8801019       
989    23867264563    397787742.7    6629796    276241.488    756.8259945       
990    23960468460    399341141    6655686    277320.2368    759.7814707       
991    24053912061    400898534.4    6681642    278401.76    762.7445479       
992    24147659042    402460984    6707683    279486.7945    765.7172451       
993    24241640298    404027338.3    6733789    280574.5405    768.6973712       
994    24335926067    405598767.8    6759979    281665.811    771.6871533       
995    24430453352    407174222.5    6786237    282759.8768    774.6845939       
996    24525286307    408754771.8    6812580    283857.4804    777.6917271       
997    24620355305    410339255.1    6838988    284957.816    780.7063453       
998    24715737515    411928958.6    6865483    286061.7768    783.7308953       
999    24811356666    413522611.1    6892044    287168.4799    786.7629587       
1000    24907283784    415121396.4    6918690    288278.7475    789.8047877
For \( \left\lfloor \log _{10}\left( {f}'\left( n \right) \right) \right\rfloor \), I made the approximation formula (which is accurate up to n = 31).

\( \left\lfloor \log _{10}\left( {f}'\left( n \right) \right) \right\rfloor \approx \frac{1}{16}\left( 62n^{2}-56n-4\cos \left( \frac{n\pi }{2} \right)+21\cos \left( n\pi \right)-33 \right) \)

which I first showed in this post.

By using this approximation, we can have a formula at wolframalpha.

\( \frac{3\text{x3 WR Avg}\text{.}}{\frac{3^{2}}{\ln \left( 3 \right)}\left( 21 \right)}\frac{n^{2}}{\ln \left( n \right)}\frac{1}{16}\left( 62n^{2}-56n-4\cos \left( \frac{n\pi }{2} \right)+21\cos \left( n\pi \right)-33 \right) \)

Note that \( \left\lfloor \log _{10}\left( {f}'\left( 3 \right) \right) \right\rfloor =21 \) with the approximation formula as well as the actual derivative formula (that's where the 21 comes from).

To get values for a certain n, just change the 2 (located on the far right of the input bar) to a different number in the input bar.
 
Last edited:
Joined
May 17, 2009
Messages
4,970
Likes
11
Location
Ponyville
WCA
2009WHIT01
YouTube
ben1996123
#14
Code:
x	y
2	0.669408
3	5.59801
4	26.6197
5	54.5381
6	154.179
7	191.958
8	-804.047
9	-5651.51
Pretty much exact for 2-7, but lol8,9.

\( y=-0.510403x^6+11.5106x^5-102.079x^4+453.215x^3-1047.51x^2+1177.21x-491.84 \)
 

Godmil

Premium Member
Joined
Aug 12, 2010
Messages
2,196
Likes
5
Location
Aberdeen, Scotland
YouTube
Godmil
#16
\( P\left( \text{WR Avg}\text{.}\left( n \right) \right)=\frac{3\text{x3 WR Avg}\text{.}}{\frac{3^{2}}{\ln \left( 3 \right)}\left\lfloor \text{log}_{10}\left( {f}'\left( 3 \right) \right) \right\rfloor }\left\lfloor \text{log}_{10}\left( {f}'\left( n \right) \right) \right\rfloor \frac{n^{2}}{\ln \left( n \right)} \)
, where

\( {f}'\left( n \right)=\text{rate of change of number of positions of a cube of size }n. \)

\( {f}'\left( n \right)=\frac{\left( 8!\times 3^{7} \right)\left( 12!\times 2^{10} \right)24!^{\frac{1}{4}\left( \left( n+1 \right)\left( n-3 \right)+3\cos ^{2}\left( \frac{n\pi }{2} \right) \right)}\ln \left( 24!^{4\left( n-1 \right)}4!^{-24\left( n-2 \right)} \right)}{{}} \)
\( \text{ }8\left( 24\times 12!\times 2^{10} \right)^{\cos ^{2}\left( \frac{n\pi }{2} \right)}4!^{\frac{3}{2}\left( \left( n-1 \right)\left( n-3 \right)+\cos ^{2}\left( \frac{n\pi }{2} \right) \right)} \)
You know what, I'm going to give JensRenders the point for the elegance of his formula.
 
Top