2009-05-16

New Pattern Found in Prime Numbers

clipped from www.physorg.com
http://www.physorg.com/newman/gfx/news/hires/prime.jpg
(PhysOrg.com) -- Prime numbers have intrigued curious thinkers for centuries. On one hand, prime numbers seem to be randomly distributed among the natural numbers with no other law than that of chance. But on the other hand, the global distribution of primes reveals a remarkably smooth regularity. This combination of randomness and regularity has motivated researchers to search for patterns in the distribution of primes that may eventually shed light on their ultimate nature.
In a recent study, Bartolo Luque and Lucas Lacasa of the Universidad Polit├ęcnica 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.

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clipped from en.wikipedia.org
Benford's law
Benford's law, also called the first-digit law, states that in lists of numbers from many (but not all) real-life sources of data, the leading digit is distributed in a specific, non-uniform way. According to this law, the first digit is 1 almost one third of the time, and larger digits occur as the leading digit with lower and lower frequency, to the point where 9 as a first digit occurs less than one time in twenty.

Prime Numbers and the Benford’s Law

[...] here is the output plot showing an extremely good accuracy claimed by paper authors
http://pyevolve.sourceforge.net/wordpress/wp-content/uploads/2009/05/prime_plot.png

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Sources:
  1. New Pattern Found in Prime Numbers
  2. Benford's law - Wikipedia, the free encyclopedia
  3. Prime Numbers and the Benford’s Law | Pyevolve
Related:
  1. Prime Numbers and Benford's Law - Steve Krenzel
  2. Lucas Lacasa homepage: ABOUT ME