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Prime numbers and the first digit phenomenon. (English) Zbl 0549.10040
The first digit property (”Benford phenomenon”) is known to hold, in particular, for the sequence of primes. The authors show that this result remains valid if ordinary relative density is replaced by a much more general type of density which they define, including zeta density.

MSC:
11K16 Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc.
11A41 Primes
11A63 Radix representation; digital problems
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References:
[1] Cohen, D.I.A, An explanation of the first digit phenomenon, J. combin. theory, ser. A, 20, 367-370, (1976) · Zbl 0336.10052
[2] {\scP. Diaconis}, “Limits of Measures of the Integers with Application to Random Number Generators and the Distribution of Leading Digits,” Memo. NS-211, Department of Statistics, Harvard University.
[3] Kuipers, L; Neiderreiter, H, ()
[4] Newcomb, S, On the frequency of use of the different digits in natural numbers, Amer. J. math., 4, 39-40, (1881) · JFM 13.0161.01
[5] Raimi, R.A, The first digit problem, Amer. math. monthly, 83, 521-538, (1976) · Zbl 0349.60014
[6] Serre, J.-P, ()
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