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Mathematics: New Pattern Found in Prime Numbers


Source : http://www.physorg.com

PhysOrg.com -- In a recent study, Bartolo Luque and Lucas Lacasa of the Universidad Politécnica de Madrid in Spain have discovered a new pattern in primes that has surprisingly gone unnoticed until now. They found that the distribution of the leading digit in the prime number sequence can be described by a generalization of Benford’s law. In addition, this same pattern also appears in another number sequence, that of the leading digits of nontrivial Riemann zeta zeros, which is known to be related to the distribution of primes. Besides providing insight into the nature of primes, the finding could also have applications in areas such as fraud detection and stock market analysis.

“Mathematicians have studied prime numbers for centuries,” Lacasa told PhysOrg.com. “New insights and concepts coming from nonlinear science, such as multiplicative processes, help us to look at prime numbers from a different perspective. According to this focus, it becomes significant that even today it is still possible to discover unnoticed hints of statistical regularity in such sequences, without being an expert in number theory. However, the most significant issue in this work is not to unveil this pattern in primes and Riemann zeros, but to understand the reason and implications of such unexpected structure, not just for number theoretical issues but, interestingly, for other disciplines as well. For instance, these results deepen our understanding of correlations in systems composed of many elements.”

More detailed information can be found in this publication:

The first digit frequencies of primes and Riemann zeta zeros tend to uniformity following a size-dependent generalized Benford's law

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