A Surprising Discovery about the Digit 1

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.

• 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 a_n=n!
• An open question: Finding criteria for data sets that obey Benford’s Law

Applications of mathematics

(MSC2010#97M99)

• 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

* a_n=2ⁿ

Natural Numbers (MsC2010#97F30)

• Positive integers
• Leading digit

Elementary Algebra MSC2010#97H20

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