A Surprising Discovery about the Digit 1

The main mathematical news

1988: Peter Schatte claims according to Benford’s Law that base-8 is the preferred number base for computer design as it minimizes expected memory storage space.

1993: Benford’s Law is applied in accounting fraud detection. Since then it has been used to analyse additional data sources.

1995: T. P. Hill proved Benford’s Law about certain distributions and justified its application to Forensic accounting.

2013: M. Nigrini analyses $8 million fraud according to Benford’s law.

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Additional Theorems / conjectures / Open questions
  • Newcomb-Benford’s law: In many sets of statistical data (of naturally occurring nature), the probability that the leading significant digit is 1 is about 30% (rather than 1 in 9).
  • Benford’s Law also holds for most other sequences of the form 1, k, k 2, k 3, … as well as for an=n!
  • An open question: Finding criteria for data sets that obey Benford’s Law
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The main mathematical concepts / Principles

Applications of mathematics


  • Benford’s Law: Application to Forensic science and to computer memory design

Probability theory, statistics (MSC2010#97K99)

  • Average
  • Data tabulation
  • Frequency of occurrence
  • Probability
  • Random phenomena

Sequences and series (MSC2010#97I30;MSC2010#11B39):

* Fibonacci series

* an=2n

Natural Numbers (MsC2010#97F30)

  • Positive integers
  • Leading digit

Elementary Algebra MSC2010#97H20

  • Asymptote
  • Logarithms table
  • Percentage
  • Reading graphs
  • Units of measure
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