Generalizing Benford's Law Using Power Laws: Application to Integer Sequences

Table 5

Best and linear best Pareto Benford fit for prime number sequences.

Sample size	PB Parameters		PB best fit		PB linear best fit
	alpha	beta	chi-square/sample size	𝑃-value	chi-square/sample size	𝑃-value
25	23.13952	2.14449	7.396%	93.30	8.407%	91.01
168	22.99754	2.28436	0.198%	99.93	0.781%	97.10
1216	30.15504	2.25800	0.175%	90.76	0.152%	93.34
9486	32.59544	2.28442	0.172%	1.20	0.084%	23.86
77736	33.26550	2.31262	0.175%	0.00	0.075%	0.00
657934	33.82622	2.32908	0.185%	0.00	0.070%	0.00
5701502	34.28132	2.34148	0.188%	0.00	0.065%	0.00