The Significant-Digit Phenomenon

The First Digit Phenomenon

If asked whether certain digits in numbers collected randomly from, for example, the front pages of newspapers or from stock-market prices should occur more often than others, most people would think not. Nonetheless, in 1881, the astronomer and mathematician Simon Newcomb published a two-page article in the American Journal of Mathematics reporting an example of exactly that pheonomenon. Newco...

The General Significant - Digit Law

It has been frequently observed that in many tables of physical constants and statistical data, the leading digit is not uniformly distributed among the digits {1,2,...,9} as might be expected; rather the lower digits appear much more frequently than the higher ones. Perhaps even more surprising, an exact distribution for this nonuniformity of the leading digits has been generally asserted. In ...

Compression Forensics Beyond The First Significant Digit

We study characteristics of the second significant digits of blockDCT coefficients computed from digital images. Following previous works on compression forensics based on first significant digits, we examine the merits of stepping towards significant digits beyond the first. Our empirical findings indicate that certain block-DCT modes follow Benford’s law of second significant digits extremely...

Least Significant Digit First Presburger Automata

1 Introduction Presburger arithmetic [Pre29] is a decidable logic used in a large range of applications. As described in [Lat04], this logic is central in many areas including integer programming problems [Sch87], compiler optimization techniques [Ome], program analysis tools [BGP99, FO97, Fri00] and model-checking [BFL04, Fas, Las]. Different techniques [GBD02] and tools have been developed fo...

Jérôme Leroux Least Significant Digit First