Benford's law - interpret the results of Pearson's Chi-squared test These are the results after applying the R - package benford.analysis

Benford object:

Data: sursa$ca_01 

Number of observations used = 134545 

Number of obs. for second order = 98921 

First digits analysed = 1

Mantissa: 

   Statistic  Value
        Mean  0.513
         Var  0.082
 Ex.Kurtosis -1.172
    Skewness -0.086


The 5 largest deviations: 

  digits absolute.diff
1      1       2798.08
2      4       1501.24
3      5        947.56
4      2        933.20
5      6        472.64

Stats:

    Pearson's Chi-squared test

data:  sursa$ca_01
X-squared = 531.34, df = 8, p-value < 2.2e-16


    Mantissa Arc Test

data:  sursa$ca_01
L2 = 0.0019637, df = 2, p-value < 2.2e-16

Mean Absolute Deviation: 0.006162794
Distortion Factor: 2.348147

Remember: Real data will never conform perfectly to Benford's Law. You should not focus on p-values! 

How can I interpret these results? Is Benford's Law satisfied?
If p-value < 2.2e-16 => the null hypothesis is rejected. This means that my data set does not satisfy the Benford's law? The graph of my data is similar with the benford's law graph.
 A: The key to interpret your results is in the last line of the print summary:

Remember: Real data will never conform perfectly to Benford's Law. You
  should not focus on p-values!

Strictly speaking, if you want to test the exact null hypothesis that your data follows Benford's Law, you will reject it since your p-value is essentially zero. But as the first plot shows, your data does not seem to exhibit any substantive, practically meaningful deviations from Benford's Law, regarding the distribution of the first digit (first plot), which is what the result of the Chi-Squared test refers to. 
As mdewey has mentioned in the comments, with enough data, even small but not meaningful discrepancies will be statistically significant. As with any statistical model, the point of using Benford's Law is not to literally accept or reject if your data follow the Law exactly: no real data ever will. Benford's law can help you in pointing out suspicious patterns in the data that might need further investigation.
As a side note, testing only the first digit is usually not fine-grained enough to detect meaningful discrepancies. In your specific case, since you have plenty of data, it might be worth looking at the the distribution of the first two digits, not only the first digit.
A: Chi square is a bad test for Benford's law. A paper by Morrow (2014) compares several tests, and I would recommend that you read it. From that paper I'm inclined to use the Euclidean distance d*N as proposed by Cho and Gaines (2007).
Morrow, J. (2014). Benford’s Law, families of distributions and a test basis [Paper]. Centre for Economic Performance, London School of Economics and Political Science.
