Caldwell, CK (2008)

Does Benford's law apply to prime numbers?

From: The Prime Pages (prime number research, records and resources) FAQ.

ISSN/ISBN: Not available at this time. DOI: Not available at this time.

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Abstract: Perhaps the most difficult to quantify question we address in this FAQ is: If we pick several random prime numbers, will they begin with the digits 1, 2, 3, . 9 equally often, or will the digit 1 be more common (as Benford's law might suggest)? The short answer, in the cases when there is an answer, is "yes, the leading digit 1 occurs more often, in fact over 30% (log₁₀ 2) of the time." And this has little to do with the "primeness" of the numbers, it is a common feature of many distributions. But we are in truly treacherous territory here--we will first define the question much more carefully, then we can explain why Benford's law does indeed apply to primes.

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Bibtex:
@misc{, AUTHOR = {Chris K. Caldwell}, YEAR = {2008}, TITLE = {Does Benford's law apply to prime numbers?}, URL = {http://primes.utm.edu/notes/faq/BenfordsLaw.html}, NOTE = {last accessed June 14, 2018}, }

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Reference Type: Website

Subject Area(s): Number Theory

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